We have a "fun" game of poker in the local pub, low stakes and everyone knows each other. In one game I was dealt my cards, as we are close together we only lift up the corners to look. I had jack 5. I was big blind so saw the flop a Jack and two 2's. two others bet and at the end of the game I had two Jacks, as had the chap next to me the chap opposite had 3 twos but as I showed my hand I realised I had been dealt 3 cards. We all called misdeal but the chap with 3 x 2s said he should have won as I should have realized I had 3 cards and the game had reached it's conclusion. Who is right
You have a dead hand. It would be ruled dead under all published rules about poker from about forever. Although in a friendly game like you describe, misdealing is not out of the question.
The reason it is a dead hand is all about adding a little security to the game. People hold out cards once in awhile, and while this particular rule won't stop a good cheat, it does make it a little more difficult, and it makes it a lot more difficult for the sloppy cheat.
In a public casino poker room, if one makes weak rulings they compromise the security of the game for everyone else. In your case if your cool with the people, know where to find them when you figure they were actually cheating you, then by all means let this one go.