Poker: The Worst Hand I've Ever Played

I'm sure it's not THE worst, but going through old hands I almost vomited replaying this one:

No-Limit Hold'em, $0.25 BB (6 handed) - Hold'em Manager Converter Tool from FlopTurnRiver.com

CO ($17.85)
Button ($100.45)
SB ($39.45)
BB ($58.70)
Villain (UTG) ($25)
Hero (MP) ($24.65)

Preflop: Hero is MP with 3, A
Villain bets $1, Hero calls $1, 4 folds

Flop: ($2.35) 5, J, 3 (2 players)
Villain bets $1.50, Hero calls $1.50

Turn: ($5.35) A (2 players)
Villain checks, Hero checks

River: ($5.35) Q (2 players)
Villain bets $5, Hero raises $10, Villain raises $17.50 (All-In), Hero calls $12.15 (All-In)

Total pot: $49.65

So I float the flop to take the pot on the turn. I turn (what figures to be) the best hand and inexplicably fail to value bet it. That's the first mistake. The biggest mistakes are on the river of course:

I made 2 mistakes here: the raise to $10 and the all-in call.

First the raise: Why on earth am I raising here? I must have been thinking "I have 2 pair let's get more money in." This is such an awful mistake. Instead of raising because my cards are good, you have to think about what you're hoping to accomplish. There are 2 reasons to raise: to make him call with a hand I beat or fold a hand that beats me. I can't achieve either of these in this situation because if he has a worse than mine (worse 2 pair or a bluff) he's going to fold. If he has a hand better than mine (a set, better 2 pair) he's going to call or reraise. If I think my 2 pair here is the best hand, I should call and not raise.

Second the all-in call: As I said in the first part, if he has a hand that's worse than my 2 pair, he's going to fold. He didn't fold, he went all-in. Therefore, his hand is better than mine. I called. Gross.

Hopefully I learned something here, either about raising on the river or about how bad I am at poker. The real lesson here is that it's important to go over old hands and think about them sometimes. You can learn from your mistakes or feel good about how you can recognize that a play you made was terrible.