There might be a shortage at the regional level because of the low starting pay and recent increases in required qualifications.

The regionals may be panicking, but the majors are not too concerned...there are a lot of 50-seat RJs in the regional fleet which will be going away over the next 5-8 years, so even if some regionals have to park airplanes due to lack of pilots the majors wanted some airplanes parked anyway.

There will likely never (in our working lifetime) be a shortage at the major airline level, ie I cannot foresee a situation where anyone with ATP minimums and a reasonably clean background would automatically get hired at a major without previous turbine time...I think there will always be more qualified applicants than jobs.

And, no don't believe anything flight schools tell you. Your career potential depends on your age, how many hours and ratings you've already accumulated, whether you have a 4-year degree, and how flexible your lifestyle is. Having significant savings or outside income stream also enhances your career prospects because it gives you the flexibility to chase career progression without as much concern for finances early-on.