To become a commercial airline pilot it makes no difference what degree you have so long as you have one.
The important thing is going to be your flight hours, instruction time and how much multi-engine time you have. The big airlines like a lot of dual engine time, it also looks good if you know how to handle a jet.
The biggest advantage to getting aeronautical science degree from an aviation school is that you will make connections with pilots who you can network with later for jobs. Can you can do pre med coursework at a place like embry riddle? I hve no idea what the curriculum is like at those colleges, but my gut tells me no tey don't have a pre med curriculum.
Most regular colleges have aeronautical engineering but not 'aeronautical science', which is basically what you will learn when you get you PP.
Also, lots of commercial airline pilots are dentists, lawyers, doctors and so on because of the nature of the work hours. so don't assume you can only do one or the other. In fact, this will become more common that we see pilots with other primary careers because we are going into an era where pilots need to pay there own way for experience more and more before they can fly or free or get paid to fly. It is normal to spend $100k in flying to land an $18k/year gig at a regional airline. (And med students complain about $200k loans).
Overall, unless there is an aviation college that has pre med coursework as well, you absolutely do not need to spend your time getting a second degree at a 'regular college' in stuff you will be studying on your own time anyways. If you're not going to an aviation college, You are better off picking a college with a good flying club, rather than having an aeronautical science program, because the people who are actually flying are the ones you want to make connections with.