Should I be worried about these warts on my hand?

I've had what I believe to be a wart on my right pinkie finger for over two years now, and just a few months ago, another, smaller one appeared on the next finger over. Once I saw that, I decided I should try to treat them once and for all the remove them. I've been using the liquid salicylic acid type of wart remover for a few months now, and I'm not sure if I'm getting anywhere or not. There have been a couple times when I thought the larger wart was gone, but it came back quickly. To make things worse, I discovered a third wart on the side my middle finger of that hand shortly after I began treating the other two. Should I be concerned about the sudden spread of my warts and my difficult with treating them, or is this normal? Could these warts be a sign of something worse or possibly not be warts at all? Any help or advice is very much appreciated. Thanks.