Steve,
If your doctor said to expect heavy leaking this is probably pretty much what he expected. By all means talk to your doctor about
your symptoms but what you describe is pretty typical for a heavy-leaker after a prostatectomy. It was several weeks after the cath came out before I could stand up, walk to the bathroom, and pee -- in that order. I could stand up, pee, and walk to the bathroom but it took a long time to get enough control to have anything left after a few steps. It was months before I could walk a mile and still have anything left in my bladder so I could stand at the urinal and produce even a squirt.
In the next few weeks you will work out coping mechanisms. You will find out how many cups of tea a pair of high-absorbancy Depends pull-ups can hold. You will probably get really mad at your surgeon. (It's a phase. It will pass, eventually.)
A few other things -- the burning at the end of your penis is probably 'referred' pain from your bladder neck which is still irritated from the surgery. (see
en.wikipedia.org/wiki/Referred_pain) The reason you seldom feel like you need to pee is because you don't. Unless you are sitting or laying down you are probably leaking about
as fast as urine is produced.
This all gets better gradually. It takes months for your body to attack the stitches in your urethra and they can be irritating until they are gone.
Hang in there. Let us know what your doctor says.