Bike feels like it is getting stuck when I start pedaling or increase pressure as I go up hills My bike feels like it is getting stuck when I start pedaling or increase pressure as I go up hills. Of course, I checked to see if the brakes were rubbing but they are completely free of the wheel. When I try to start riding after a stop I get the rubbing noise and feeling of tremendous friction but once I reach a constant speed it disappears. It will reappear as I speed up quickly or climb a serious hill.
To summarise the comments, it sounds like your rear wheel has some freedom of movement where it shouldn't.

If you stand beside the bike and wiggle the top of the tyre sideways, can you perceive any movement?  You shouldn't be able to feel anything.

Try the same sideways push at the front or rear of the rear wheel.  Again no motion should be detectable. 

I'm going to go with a broken axle, a loose axle nut or stretched skewer, or a bearing problem that is permitting lateral play in the wheel rim when under load.

Good news is all this is fixable.  Take the rear wheel out and start investigating, and do let us know what you find.