Here are my thoughts as a 34 year old engineer and part time CFI. I instruct, tow, fly gliders, and pretty much can be in an airplane whenever I want. The day job still wins, hands down, compared to an airline gig. You have many options in medicine, many that don't actually involve practicing medicine in any way, that still pay handsomely. You can work out a schedule that lets you fly as much or as little as you like.
Coming from someone that could fly full time right now - it isn't worth it.
If you really have your heart set on it, fly on the side. Find a glider club, fly a few hundred hours there. That shouldn't cost you more than a few thousand bucks. You can add the commercial airplane and instructor ratings to the glider ones pretty quickly. Then get a CFI, teach on the side for a few more years. After that, when you are done with med school, you'll have the time for an ATP. I know a doctor that is a CFI... Very do-able.