I am not sure if I would translate "hasta la piel" as "even my skin", it does not make sense to me... maybe "on the skin" might be better.
I think 'me duele hasta la piel' seems like 'doer na pele' (Portuguese, since both of two languages have common aspects). If it is the same as 'doer na pele', then it means something that hurts you a lot. It does not literally hurt your skin, but the pain that something or someone inflicted to you feels like it were hurting your skin.
But, once that I am not sure if the expression looks like Portuguese, feel free to discard it :)
* 'doler hasta la piel' literally translates to 'to hurt up to the skin', this refers to something that hurts you a lot emotionally.