Hi and welcome!
I don't have any concrete answers for you, but I've heard from a lot of women with AVM who couldn't tolerate birth control pills. I think it's going to have to be your decision ... is the pain so great that you'd rather have another birth control option?
Others may chime in, but this forum is a little slower than the others. You might want to ask an expert here: http://birthmark.org/experts.php
Good luck and let us know how things go!