(FYI /- I'm not a boxer... I train in full contact karate and do a lot of target and bag work, normally without gloves or wraps - just saying because gloves bring their own safety risks when it comes to your hands as you can't form as tight a fist, so actual boxers may have some further insights there. I've been teaching martial arts since the 80s on and off. Day job C++, 40s...)
Firstly, stress itself can cause fractures even if your technique's ok - it's a huge shock to the body to go from nothing to punching as hard as you can in a month or three. So, ease into it... back off now while you're sore, then try to find a gradual increase of intensity that doesn't crosses the line to regular discomfort or injury.
For wrists, I recommend trying to improve the stabilising muscles in the wrist that prevent the wrist bending when you hit something... one good way to do so is to get in a pushup position (doesn't matter if the body's just off the floor or all the way up) while only the last centimetre or so of your index and middle finger knuckles are supporting your weight - do not let the joins near the middle of your fingers touch the floor... the idea's to get to the stage where that's no effort and you can do it for as long as you like - until then, just do what's comfortable without getting to the point where you just can't keep the wrists straight.
If you have some weights, rest your elbow and forearm on any surface - wrist just over the edge, hand facing first up then down, and do some sets of dipping and lifting the wrist.
Pushups on your finger tips will help too - in fact pretty much any pushup position. Slightly more intense - you can find a wall or other surface about waist high and push down with your knuckles to lift you off the ground - again trying to make sure only the last centimetre of your knuckles touches the surface.
As well as strengthening, consider how you're hitting - experiment a bit on the bag to find out which angles are comfortable and solid - where you can feel the same part of the fist you were touching the ground with during the pushup position above biting in to the bag while the wrists aren't strained. For example, relative to a line between your head and the bag, you might find you can hit with a bit of a hook coming in to the bag about 45 degrees much more comfortably than at ~55 degrees... get used to the comfortable angle and try to keep to it during classes. If you have to hit at a less comfortable angle for some reason, hold back a bit on the power. You may well find the hook angle that's comfortable's different for a vertical fist position (i.e. palm facing sideways) vs. horizontal (palm down).
For any punch on a target, you can squeeze the forearm a little as you hit to stabilise the wrist, and start slowly - gradually increasing power as long as you're feeling stable... (once those muscles develop you can stop the conscious extra squeeze thing as it'll be reducing your speed and power).
For elbows - well - you might decide to compromise on the following suggestion later in order to your elbow tucked in protecting your ribs / liver longer, but until you've got a really good punch, and when you want maximum power, just avoid letting the forearm swing outwards to straighten or lock the arm. Not only does doing so cause injury, it degrades power. Most of the time, consciously move your elbow and hand along the same line or curve towards your target. Put another way - after your backswing, if you were punching towards your opponent's head, they'd just see your fist with the elbow hidden behind it. If you get used to this, the elbow won't be wanting to straighten 100% anyway... punching full power, I lock not into a straightened elbow position but into a naturally "tensed-muscle" position a few degrees short of the elbow being fully locked... it's not "holding back" - just a consequence of technique.