possible wart not responding to treatment

so, i've had this bump on my right knee cap since elementary school. im now in college and i finally decided to go to the doctor so he can take a look at it. i always thought of it as a wart, but a funny looking one. i kow what a wart looks like, but mine is about as big as a dime, brown around the edges and white and dense in the middle. i always try to cut it with nail clippers but it always grows back. when i went to the dermatologist, he looked at it and wasnt sure if it was a wart or not. but he freezed it anyway. so when it puffed up, i acidentally popped it at the beach. i could tell it didnt go away, just the top layers did. then i went back and i told him it didnt go away, so he did this thing where he numbs it and scrapes if off. i had to wait a good couple of weeks to go back in the ocean. but i noticed it was still growing!! i wanna go back, but i dont wanna waste my time and money. is there another solution? and does anybody know what IT is?!