Tattoo help. so confused!!?!?

i got a tattoo last summer. i hate it so much because it looks like it was drawn with a crayola marker. it is STILL puffy and when the skin peeled off, there were actually bits of skin with no ink on it. i never got it touched up because i was afraid they didnt know what they were doing since something obviously went wrong. the tattoo place has mostly 5 star reviews on yelp, so i know they arent known for being bad. my theory is since im young, small girl, they took advantage of me and let an intern tattoo me. i desperately want to get my tattoo removed now. is it possible that i am allergic to tattoos? also, share what you know about tattoo removal. the tattoo is turqouise and about the size of a quarter, and on the top of my wrist