There just hasn't been enough deep discussion about why Sam didn't look for Dean. It's been glossed over and hardly anyone is talking about it (I'm surprised how unnoticed this has gone) so I've decided to give you some deep and very very serious meta and visual evidence about what's going on.
glovered mentioned something on her journal that is SO awesome that I think it needs investigating further.
I give you the case for why Sam's memories are false and how Amelia is actually Dean.
Let's start with this crucial observation from glovered's journal.
Sorry but omgggggg when Sam chooses to go find Amelia he walks into the room and he's WALKING INTO HIS OWN MIND. HIS SHIRT MATCHES THE WALLS. OH GOD I WANT MORE MAKEOUT SCENES NOW BC IT'S SAM MAKING OUT WITH HIMSELF.
See the evidence! It's the EXACT same pattern! This is a MAJOR clue that this is all in Sam's mind. Personally, I think no more proof is needed but I shall provide you with clear evidence that not only is it all in Sam's mind but his "memories" have been manipulated, I believe, by the angels. They've allowed him to create this fantasy. There is also so much evidence that Amelia is in fact Dean that it's actually rather embarrassing in it's obviousness. We don't exactly know why yet, but I believe that will be revealed very very very very...er..very very very very very soon.
Time to examine the evidence.
Let's start with the strongest signifier. Show went to a lot of trouble to make the room number clear. It's a sign!
Room # 118
Amelia's room is No 118. A very potent number. It symbolises a number of things:
It "symbolises a latent potential, unknown, but working actively to appear". source
"Angel Number 118 is a message of encouragement and support from your angels". source
Clearly the angels are manipulating Sam's mind. Making him see positive things. Making him try and forget Dean. But Sam is holding on too tight. The imagine of Amelia the angels have given Sam has been re-created in Sam's mind to represent Dean. This is evident by the fact that:
Amelia wears the same clothes as Dean:
It's curious that in both these cases Amelia is dressed like Dean was when he was in a hospital. I think this might be a clue as to where Sam might be residing during these hallucinations.
The red checked shirt is very significant. That's Dean's "angst' shirt. Sam may be living the "dream" but underneath it all is the angst.
Amelia drinks like Dean:
Amelia is obviously an alcoholic, evident by the all the beer cans stacked up, whisky bottle and an empty margarita glass. Sam can only imagine being around someone who drinks as much as Dean. It's familiar and comfortable. ALSO... look how neatly those cans are stacked in the corner. This is Sam's mind trying to make sense of this world. Sam likes things ordered and neat (remember in Mystery Spot when Dean died? He lived in a very tidy, ordered room).
Limes are mentioned a lot in this scene. Limes are a symbol of resurrection. ("It is a symbol of life, vitality and energy; resurrection." source. OBVIOUSLY this is Sam wishing he could find a way to resurrect Dean.
There's no way any motel could look THAT fugly: (well, there is but let's ignore that fact)
Seriously! Those curtains and that bedspread totally clash! And look at all those flowers surrounding Sam. There's clearly something not right here. His poor brain is in such a muddle he can't even get the decor right. Plus...it looks like he's wearing a skirt. A big, flouncy princess skirt (I am sure there's some psychological reason for this but that's very serious meta for another day). The white shirt symbolises his mental state. He's probably wearing that in the mental institution he's in. Poor boy.
Also, look at that room. It's just a bit too tidy. It seems strange that Amelia would keep the room that tidy and not throw away the beer cans. (Unless of course they were all from the night before, then I suppose that's reasonable). It's also note worthy that they "met" in a motel. This is where Sam and Dean live. In Sam's mind she has to be in a motel because that's what he connects Dean with (I won't even touch the fact that he's had...er...relations with Amelia. You can let your mind take you there if you wish).
I realise that no further proof is required but I'm on a roll, so let's keep going.
The picnic is OBVIOUSLY totally imagined because who lives in those colours? With everything slightly blurry?
In the scene Sam is surrounded by green. A symbol of: "Love, joy, abundance, hope, youth, mirth, gladness, resurrection, spring". source RESURRECTION AGAIN! They are hitting us over the head with all these clues!
This scene starts on a bridge. This is a metaphor for Sam crossing from his real life state to his "dream" state. It's also important to remember that moment when Dean body-slammed Sam on the bridge in the Pilot. Sam doesn't forget heart stopping moments like that (who would!?!). Bridges symbolise the power and passion of Sam and Dean's relationship. (I could go into this much more of course - the bridge sometimes being strong, sometimes rickety - just like their relationship, but that's another important meta for another day).
The cake is very significant I believe. Look at it! Obviously fake - almost a cardboard cut out. How did she manage to carry that cake there in that picnic basket? It's obviously a construct of Sam's mind. I should imagine that Dean once bought a shop made cake like that for Sam once on his birthday. If this was a real moment the cake would have been hand made by her. Everything else is "perfect" except that. And what is she wearing? Oh Sam, your fashion sense. /o\ No wonder you started dressing her like Dean later on.
What's in a name?
The dog's name is Riot! A DEAD GIVE AWAY! TPTB think it's a riot leading us down the garden path (much like Riot did) believing that Sam would not have looked for Dean when he disappeared. They are having a laugh at our expense.
ALSO: (VERY IMPORTANT!) ... there is a band called RIOT and it stands for "Righteous Invasion of Truth" (source) NEED I SAY MORE!!!
The meaning of the name Amelia means "striving". (source SEE! Striving to convince us that she is real.
What's in a painting?
If any more evidence is required then just look at that painting Sam is under.
In dream interpretations the water and the sea are HUGELY symbolic:
Water can often symbolize the unconscious or the soul. What might be lurking under the surface?
The ocean may contain what one perceives as danger, such as lurking monsters,
A Very Reliable Source
And lastly, there's the fact that all of the lamps in this motel room appear in other motel rooms in Sam's life (you'll have to trust me on this) obviously means he's bringing back those memories. It might even be symbolic of Sam trying to "shed some light" on what's going on. Very clever show!
Examining all this evidence makes it absolutely CLEAR that show knows what it is doing. It's had a plan from the get go. Sam WAS looking for Dean but got sidelined by these pesky angels intent on thwarting his progress.
Happy Thanksgiving to all. Even to those who don't have it as a celebration (like us in Aus). Giving thanks can never be a bad thing. I'm thankful so many things. Not least...all of YOU LOT! <3