I don’t think medicine is blocking anything that God sends you. God “sends” illness in a sense that it is the logical consequence of a bacteria or whatever, and the response of your body. Illness is not a punishment, and not always a warning. When this is a warning, my understanding is that your mind will be enlighted to understand it (because of the lengh of it, or the particular pain it involves, the thoughts it gives you and so on).
My take on medicine is that it sure helps at times; I still avoid it, since I trust my body to heal itself, if it is a cold or so, and i know my health is ok.
In monasteries for instance, something like meat is seen as a medicine. Monks and none are generally vegetarians (because of the meaning of meat in relation with Christ, but primarily because it is seen as something rich and not needed). Not every order though follows this. Trappists are stricts vegetarians, and others would use meat to regain strengh during or after an illness. So medicine can be seen as blocking penance (?) or an opportunity for healing (redemption ?). But I don’t think it is wrong at all, in itself.
My priest who is a Franciscan takes medicine but has the same view as I have. it is not wrong, but as anyone, religious or not, would presume, you take something which is not always natural, so then you have to decide if it is needed. He had back pain. He took something because the aches were too strong for him. and he didn’t feel like he didn’t take what God sent him.
Oh I just read a post above about Paul: well, Paul talks about Luke as the beloved physician…

. About the Lord Himself, why would he cure people? It is true “it was for the glory of God to be revealed”, but still this doesn’t say we should counter illness, even if it is a part of sanctification and of our sinful nature.