So even the professional artists I know have a day job...I don't see any reason you can't do science and art simultaneously. I agree that you'll need at least a masters in science for that...I have a phd in microbiology. The job outlook for science is not super...ie you're not likely to end up a professor running you own lab but can work for someone else and be part of a team effort( of about 50 grad students trained over the five years in my program I think 5 are tenure tracks profs).

Lots of people I know working in the lab do art and it's beautiful...none of them professionally but there is no reason why that couldn't happen. Again some of the professional artists I met felt crushed by art school and realized afterwards a degree is not necessary in that field unless you want to teach etc.

Anyway I do research on intestinal bacteria but at the same time here is my deviant art profile....admittedly not updated for a while despite lots of new work...

Sally599's deviantART Gallery

I enjoy it more as a hobby so I haven't worked hard enough to make it look professional but that's the great part of it not being a career....I don't have to do anything I want. It may be that pet portraits are selling well...if you're in it for the money you'll do what people will buy instead of what you most want to do....

Also FYI I don't know about Greece but in the states if you're getting a phd the school will typically pay you a stipend in addition to comping your tuition...so it's not more debt and although the stipend is very low you can live on it.