Drilled hole through wall stud
With no more specifics than that I would say you should have no concern that one 3/8 inch hole drilled through one stud could present any structural problem. There is so much redundancy in standard stud construction that there is a vanishingly small probability this could have any practical consequence.
If the hole is where you want it and it is not on the edge of the stud, then use the right size of plastic sleeve anchor and screw in this hole to hold the curtain rod. That would be stronger than a toggle bolt into drywall.