Playing Doctor and Heal Thyself can be done together though Heal Thyself will be unlocked first simply because you need to cure yourself at points where you must.
You will need 100 Cases of Meds and 300 Blood Plague Samples to craft 100 Plague cures, you may reasonably need to craft more just in case you used it on yourself otherwise you're in the process of doing it earlier than going through this guide.
Easiest way I did this was having a follower follow me and both carry cures after farming for the materials. Then walk into the wall and switching to my follower and tell them to use the cure.
You basically have them both walk into the wall and out to gain plague and tell each other to use the cure than on yourself. Two birds, one stone.
Build an outpost nearby just in case