sorry i should have asked for ur stack as well but anyway.
knowing what u did and what came out you were proberly right in folding.
as you do not know what the other person has so you have to go with ur gut.
plus never belive what other players tell u they had they will be lieing 90% of the time.
as for the way you played that hand, the raise preflop was a good 1.
as for the second raise there should have already been 3600 in pot so really u should have raised a minimum of 4k there.
cos i do not know ur stack i cannot say what you should have raised here, but the way it sounds is the other person acted first.
cos of this you should have raised again here if your stack was big enough 10k if it did not put you down to a major lose, minimum would be 5-6k.
you said he told you that u had the winning hand is proberly correct but cos you checked in this position it showed the opponent a weaknes
like you had nothing or was hesitating giving him the opertunity to push and scare you on next card, and cos it was a low card he pushed thinking u never hit.
but in all terms for somone new to game i would say what you did was not a bad thing, cos if he is calling he has noticed you have weak habits or he had an ace with a low card.
just think of it as a learning exsperience.
hope this helps in anyway