Had strep. Finished meds (z pack/prednisone). Week later, sore throat again + bad headache (I have migraines). OTC no relief. Urgent care or wait? Thx

Urgent care. why wait and suffer with the headache? Also check to see if the Z-pak took care of the strep as sometimes you may need a re treatment or different antibiotics.
Viral infection. Concomittent viral infections in throat, on top of strep are quite common and may have been exacerbated by steroids you took earlier. I would give sometime before another trip to Urent care center for another round of meds, that may not be indicated. Just use ibuprofen or chloroseptic spray/lozenges for symptomatic relief, along with plenty of vit C and fluids.

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