I mudded over some drywall seams but some of them are uneven and the mud is very thick in some areas. I thought they wouldn't look very obvious after painting but it looks awful. Now I'm not sure whether I should sand things down more and paint again or use more mud, sand, then paint again. Help.
I would sand down the worst of the high spots and then get a nice wide (12" at least) taping knife and some light white mud and go over it ....may have to scrap or even sank a bit between coats ....but it just takes practice . I've done this in a rental that had a terrible wall w/lots of damage, it took a few coats but it turned out good. A good wide taping knife is your friend! When applying the mud, try to press on the knife so that it's SLIGHTLY pressing down more on one side than the other and work backwards from there. You'll get this! just takes practice.
Paint doesn't sand well. It balls up and makes a worse mess of the wall. Coarse-grit paper will do the job, but then you need to skim to fix surface texture.
If anything, scrape off any lumps with a taping knife to minimize the skim depth needed. I don't see anything in your photo which calls for that, though.
I would skim this with a wide knife (12" or larger). Press firmly and scrape over the high areas to fill the low areas. Taper out to the sides. Let it dry, then use a light at a low angle to inspect. Repeat as needed. Final sanding should be light and minimal.
Then prime and paint.
I'd sand it down to get it smoothed out then go over with one or two more coats.
It's still some work, but it will come out better than if you just start adding more mud as-is.
If you go over it as-is with more mud you'll need to build everything out, which takes time and more mud. Furthermore, going over pre-existing paint will result in the mud "bubbling" due air not being able to "escape" to the drywall properly, this will result in more sanding and coats. You'd also be left with a situation where the mud might not be adhering to the wall properly, leading to cracking in the future.
As long as you used general-purpose or topping mud, you shouldn't have much issues when sanding once you get the paint off.
When sanding drywall mud (and paint) be sure to wear a mask, specifically an N95. I personally wear a respirator with a P100 general purpose filter so I don't have to worry about what else I'm sanding.
If you can get some of the "edges" smoothed out and some of the paint off the wall during sanding I'd plan to apply 1 or even 2 coats to even things out. The further out you go the less noticeable any humps will be. Its not clear how this originally was built out, but just in-case the usual flow would be taping the joint, then 2-3 coats. Assuming your DIYing this with general purpose mud, each coat takes 24 hours, with the possibility of also including a "prefill" step ahead of taping to fill larger gaps between the drywall. Unlike professionals, odds are we aren't going anywhere, and general purpose is very forgiving in regards to sanding and drying time. With multiple coats you always can apply more or sand as needed, don't expect or aim for it to be perfect with just the taping layer. General purpose is forgiving, but also will shrink more after drying, so expect to apply multiple coats.
You'd also maybe want to get bigger knife for these coats as well. It isn't clear from the picture what you used originally, but assuming you used a 6 inch, or maybe even a 4 inch, I'd go bigger to 8-10-12. With a bigger knife its easier to flatten/smooth out the space. Professionals would use a metal/steel knives, or a trowel, but if your just patching a few holes and doing a little taping, a set of plastic one will suffice, the main thing is having the right size to flatten things out. Start smaller (6 inch is the most common) then use bigger knives for later passes. I personally have a 4, and 10 metal knives and a 6 inch plastic one, for no other reason than that's what I was given. Plastic will bend, possibly not leave as smooth a finish and degrade faster, but it will get most jobs done before then. (plus they are cheap)
The final aspect is the right technique. To utilize the knife properly (regardless of size) you'd want to feather your edges by apply pressure to your knife on the outside, or away from where the tape is to "push" your mud toward the tape. The amount of pressure you apply will increase with each coat, where the last coat is there to really flatten things out, and thus you'd want things as smooth as possible. This is easier the bigger the knife is, and can help you gently build transitions between the pre-existing wall and where your taping and building things up. It takes a little practice, so if you want to nail it down I'd suggest takings some spare drywall and practicing on it.
Just keep in mind you can always add more mud, and you can also sand things down. The aim is to strike a balance of building things out elegantly while still leaving some "on the wall" that can always be quickly sanded down for a smooth and flat finish. Unless your in a rush, general purpose should be good enough, is forgiving to sand and can be used for all steps, just be prepare to wait between each coat.
PS. If for some reason you used a hawk and trowel for this the same advice still applies, but next time tape using a knife then bring in the hawk and trowel for the last few coats to build things out.