There’s a difference between working a muscle hard (post-gym soreness), working a muscle too hard (overtraining it), and problems like RSD, which often don’t affect the muscles at all. Tennis elbow, for instance, is a problem usually affecting tendons in the elbow. Despite the name, the third category - thingss like repetitive strain disorder and tennis elbow - are not caused simply by overworking the muscles or joints, they’re caused by repetition coupled with improper form or technique, or some sort of one-off trauma. What probably happened with your tennis elbow is that when you were stretching the canvases your technique was slightly off - maybe you were snapping your elbows into it a bit, something like that. That creates slight tears in the tendon which then get exacerbated every time you continue the motion. That’s why it happens a lot in sport - a tennis player ‘snaps’ into a shot one time and slightly tears their elbow tendon, and when they keep repeating the same shot it gets worse.
Now with the gym, as long as your technique is correct and you warm up and warm down properly, that problem shouldn’t ever happen, no matter how hard you work your body. It’s a good idea to get someone to show you exactly how to do each exercise you’re planning on doing. When you’re lifting weights you should do it at a moderate speed, with the same speed both for lifting the weight up and for putting it back down again (about 1 second each way). If you lock your elbows or knees at the end of an exercise - and personally I think it’s a good idea to do so as long as you do it right, because it helps strengthen the joints - do it very carefully. When you’re doing those “pulling” exercises, it’s very easy to pull up the weight and then just let it go on the way down. I strained my elbow tendon doing that. You need to get the proper form and do each lift at a moderate pace and carefully. If you need advice on form for any particular exercise let me know, or ask someone in the gym.
Post-gym soreness is something different. If you have the correct form in the gym you shouldn’t ever have problems like RSI, no matter how hard you work. But post-gym soreness is normal for proper workouts. You should only ever feel post-gym soreness (also called DOMS, Delayed Onset Muscle Soreness) in the muscles, not in the ligaments or tendons - if your joints or lower back feel sore after a workout that’s a problem, and it probably means your form isn’t right. But if your muscles are a bit sore the next day that’s a good sign. The conventional wisdom is that when you work out properly you are supposedly creating microtears in the muscles; your body heals them, building them back stronger than they were before. With DOMS you usually don’t feel any soreness at all straight after the exercise: you gradually start to feel it over the next 12 hours, it peaks after about 24 hours, then it subsides and disappears after about 48-72 hours.
It is possible to “overwork” a muscle, the second option I mentioned at the start. That’s when your form is fine, but you literally overwork the muscle. It’s basically just DOMS, but gone a bit too far. Again, you would only feel that type of pain in the muscle, never in the joints, and overworking a muscle isn’t a big problem compared to RSI, you’d just have to rest it for a few days and the pain will subside. If you build up your workouts slowly, establishing your limits, and don’t try to do too much too soon, overworking the muscles shouldn’t be much of a problem.