You and your doctor should discuss if the medication is still worth the risk
If your doctor believes you should stay on the medication that may be causing a reaction, they will sometimes prescribe antihistamines so you can continue on without reactions to the same extent. When you are suffering from severe reactions, but require the medication, sometimes steroids will be prescribed.
Sometimes, even if medications do not cause the skin problems themselves, they can make a person more susceptible to other skin problems. So, you may find that under certain medications you will be more prone to bruising, or at a high risk of sunburn if your skin is not protected properly.