I don't know what pump you have, but a couple of points from what you've said.
The pump should seal against the pubis area, not against your penis. You use a gel/lub to make an air-tight seal, although you might need to do a bit of trimming if you have a large bush down there (but you don't need to shave it all off). It should not be gripping the penis. You might want a bit of gel on the end of the penis if it sticks to the tube wall as it expands, or hold the tube so it dangles at an angle not catching the tube wall. There are non-medical pumps around which seal against the penis, but that's not usually comfortable, and is going to be less effective.
There's an initial training period of 2-3 weeks during which the pump is uncomfortable for most guys. During this period, you are just getting the penis used to being expanded in a way it never has been before. You slowly pump it up, just doing a one hand crank on the handle and waiting 5-10 seconds until that's drawn in blood, before you do a bit more. When you've gone as far as you can, let it down, and repeat the procedure. Keep doing this for 10 mins per day. Don't fit a constriction ring or try to have sex with it at this point. After 2-3 weeks, the discomfort should have gone, and the training period is over.
For penile physio/rehabilitation, you basically keep doing the same as during the training and again without a constriction ring, although you can leave it pumped up for longer before letting it down, but it's still a good idea to do it several times and not just pump it up and hold it for the full 10 mins. That wouldn't do any harm, but pumping up and down will get more fresh blood into it, which is part of the aim. Do this for 10 mins every day, or 15 mins every other day, but not less often.
If you get any bleeding, let it down immediately, and gently pinch the area that's bleeding to stop it. Then avoid using the pump again for a couple of weeks. Pumps shouldn't be used by those on blood thinners (except possibly low dose asprin, but you should ask for medical advice on this). You shouldn't be getting any chafing, that would suggest you're doing something wrong or the pump isn't suitable.