wear and tear = osteoarthritis. RA is inflammatory disease and much more common in the young. OA will usually be secondary at such a young age ie you're right, wear and tear is not a complete explanation for a 25 year old. unless you are a world class tennis player? 
I have severe OA in my hip, diagnosed at 19, but it's secondary to avascular necrosis (problems with the blood supply). To diagnose OA you need at least an x ray and preferably a scan or ultrasound to see what's happening in the soft tissues too (to diagnose RA, I think you need a blood test). But you may well not have OA yet - the symptoms you describe could be repetitive strain injury type problems.
The shoulder is the most unstable joint in the body, structurally, and it may be that you've been using it in an odd way for some time. at minimum, your doctor should send you for an xray to rule OA in or out, and give you a physio referral so they can assess how you're using the shoulder.
The pain in your wrist is probably referred pain, which is really common in chronic pain conditions. Essentially parts of the body that are closely connected to the problem area in your nervous system will experience severe pain too, as the nerves jangle and misfire. Sometimes the pain in my knee (which is fine) is far worse than in my hip).
For managing the pain - you learn what works for you over the years. For me, avoiding certain types of use, warm baths before bed, hot water bottles, yoga, 600mg ibuprofen (good strong dose!) on bad days to aid sleep.... diet and supplements also well worth a look. An alkaline diet reduces inflammation in the body, and chilli, garlic, ginger, turmeric are all very good. Supplements: oils, turmeric, boswellia, among others.
Good luck OP. Go back to your doctor.