Do both.
College will open up more pilot jobs. Some airlines only hire college graduates.
College will also open up other career paths that you may need when flying jobs are not available. I recommend you NOT get an "aviation" or "airline management" degree; get a mainstream degree (engineering, computer science, economics...) from a real university.
You might be able to work on your Private Pilot license while in college, as well.
Unless you get hired by a major airline, flying is NOT a lucrative career. For every pilot that is making over $150K/year, there are probably 100 others making less than $50K. Find a lucrative career and fly as a hobby.
You didn't mention it, but military flying is one good way to get great flying experience, and get paid to do it. You have to want to be in the military, though...