If you are minded to do a degree (and you can afford both degree and flying) then certainly do a degree, but don't do an aviation degree.
Do a BSc - generally respected, and gives you a teaching opportunity.
Do an MBA - generally respected, and will help later in your career should you want to "progress" to management.
If you have the marks and interest, then certainly law or economics would likewise help, and give second job prospects.
Medicine requires too much initial further training commitment to be particularly useful, IMHO.
I went to three universities, on a BSC and a BEng (Chem) and didn't finish any of them. I have never worried about not having a degree for my aviation career (I am a 15,000 hour 737 Captain) but I have regretted not completing the degree.