Prop shop advice for non-target graduate w/ biology degree

Hello everyone,

I graduated in the spring of this year with a biology degree from a non-target state school in Texas. My GPA was a 3.6+. I am a very math inclined individual who only chose biology because I (incorrectly) thought it would help with medical school admission (it really doesn't FYI.) I am reconsidering my aspirations to become a physician for numerous reasons but only if I have a shot at being competitive for some prop trading firms or quantitative firms. So I am here for advice about my chances. I know I that my chances at any of the upper tier prop shops and quantitative funds are zero because I am from a non-target with a bio degree but I am wondering if I can be competitive at any decent prop shop? My critical thinking, mental math, and problem solving skills are strong along with my deep interest in the field and desire to succeed.

When/Where should I apply? I don't have any preferences regarding what I want to be trading (options, commodities, FX, equities, etc.) I just want to know if I am at a significant enough disadvantage where applying to prop shops would be a waste of time. If you have any recommendations about where to apply, I'd love to hear them.