It's complicated.
In certain markets (such as yours) there is absolutely no doctor shortage. In fact, there's a glut of doctors in say, Boston, San Francisco, Portland, parts of NYC, etc. That's why doctors in those areas make substantially less money than they would if they worked outside of them. If I moved to one of those cities, my pay would probably go down 15-20%.
And yet, there's absolutely a shortage, for primary care and for specialists, in huge swaths of the country. I could practically double my salary tomorrow if I wanted to move to rural Texas or to Wyoming.
So is there a shortage or is there no shortage? These facts are difficult to reconcile. There is certainly a maldistribution of physicians - if you were a Stalinesque central planner, you'd probably move some docs out of Manhattan to central Texas. But if we perfectly distributed all of the current physicians, would there still be a shortage?
Maybe. Every person who does that analysis gets a slightly different result, mostly dependant on what answer they want to get and the time spans you're looking at. You can look at white papers for physicians as a whole and for specific specialties to see the numbers. For example, for surgical specialties, from a report done by the government (probably as objective as you can imagine):
https://bhw.hrsa.gov/sites/default/...rch/projections/surgical-specialty-report.pdf
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It estimates a shortage of ~10% of general surgeons by 2025 and further shortages of everything but colorectal surgery. You can read the assumptions they made in the paper itself.
I personally think we will have shortages overall and of specific specialties in general, which will be worse in places where no one wants to live. But you could reasonably argue that the overall number will be OK but poorly distributed.
Regardless though, that won't help the people of central TX.