DO you have wrist wraps? If not get some, these will help reduce the pressure you put on your wrists when lifting and thus reduce the inflammation you suffer from training. As well as regular wrist wraps get a pair of the variety with power hooks attached. Most people use these when doing dead lifts at weights their grip strength can’t yet support. Again, I think these would work well at reducing the stress you put your wrist under. The down-side to using this equipment is that your grip strength, and overall arm strength, will suffer.
To counter act this I’d include some grip work at the end of every training session. Targeted grip work, by building up forearm and hand strength, will also help with your injury. Stronger muscles in the area surrounding your wrist means these muscles can take over a lot of the pressure being put on the injury both in and out of the gym. After 3 years if your still suffering to the extent you say you are then this will take a long time to do as you’ll have to start off with light, short work and build up slowly so as not to aggravate the injury further. If you have a physiotherapist, and if they’re any good, they should be able to prescribe exercises to get you started, but I recommend you get some grippers (I use captains of crush from Iron Mind) as well as Iron Minds hand health kit.
Anyway, apologies for going off on a bit of a tangent, back to the question at hand. Rep ranges will depend on what kind of training day your doing i.e. a Max effort (ME) session will usually be 1-3 reps per set working up to your 1RM, supplemental work with your ME lift I would recommend be in the 3-5 rep range for 3-4 sets.
If your doing a Dynamic Effort (DE) session then you should working 3-5 reps of 3-4 sets lifting around 60% of your 1RM for that lift (as you get stronger and your body learns to recruit more muscle fibers for this % will actually drop down to 40-50%). For a Repetition Effort (RE) day, your current ranges look OK to me.
I would recommend you do a flat BB Bench Press, it is one of the top three lifts that should not be ignored. In my opinion an incline DB bench is a good supplemental exercise for the Bench Press. For your Pull-Ups, even if you can only do Sets of 1 rep, I would also recommend unsupported lifts and build your way up, you’d be surprised how fast you can build up your strength in this way as opposed to a supported lift.
Anyway, hope I haven’t overloaded you with too much info and given you something you can use, happy lifting.