Brakes starting make screeching/grinding noise really bad even when not braking.

I can't hear your noise or see your car from here to say for sure. But, with any unsure issue even remotely possibly related to the brakes, I'd say that no, it's not safe to drive pending inspection to find out what is going on. Taking a chance on your life -- or the life of other innocent people on the roads -- isn't worth it.