Am i paranoid or why do i feel guilty when i am innocent!?

i was VERY drunk one night and i think i may have said something i shouldnt have whereby i said that I did something when in fact i didnt do this thing!!! Now i am extremely paranoid about it. What I said (if what I think i said is what i said) is not true i am completely innocent but since that night people have been looking at me weird and making little remarks in a snidy manner and now i am super paranoid!!!! I now try and avoid public places and am just paranoid that EVERYBODY knows...is this normal...the thing that hurts me most is that its not true and that I dont know what I said cos i was drunk and if i did say it.....i have spoken with my dad and he says that i am just paranoid and that only small minded people will make something of it. however i still feel guilty and that people are judging me and paranoid.....this must be the worst explanation of something ever but im really down about this and CANT talk to anyone!!!!