Your symptoms suggest that your space heater has gone bad. Your GFCI is often on one of your 110-VAC breakers. So the first thing I would do is unplug your space heater, and then try to reset your 110-VAC breaker and if it resets then you should also reset your GFCI.
If your 110-VAC breaker still will not reset, then it may have been damaged, or you may have a short in the receptacle the space heater was plugged into.
And also you should make sure your space heater is one designed to be safe. For instance, it should be a "ceramic heater "design that is less likely to short out. It should be one that is designed to turn itself OFF if it is tipped over, and it should be UL Approved which you can check by the UL label on the unit, not just on the cord, but on the unit.