ANSWER:

This is permissible. 

You should also try cupping as it is very beneficial for your headaches. 

I work in a hospital. And I have the issue of repeated episodes of headache, sometimes very severe which impairs my work. My question is, during fasting, can I use transdermal patches of painkiller medicine which are placed on skin and the drug gets absorbed directly through the skin into blood?

Fasting |