Clam yo tits everyone. Yes OP is a dumbass, but this is not a huge deal. Drain, flush (several times well), and fill your radiator.
Here's a semi DIY.
I would also say, do it your damn self, cause a shop is just gunna do a drain, quick flush, and fill. Not the thorough flush that you want. However, you ARE the one that put oil in the radiator in the first place, so herein lies our conundrum.