Your muscles are going to get stronger way faster than your joints. A lot of holds that are ~V3 and up (depending on how your gym grades things) will end up putting a lot more strain on your finger joints/ligaments than the big, juggy kind of holds you see at the V0-V2 range. If you’re having trouble with really crimpy holds, that’s probably a good thing if you’ve still only been climbing for a couple of weeks. You really don’t want to sprain a pulley tendon, it sucks.

So, for now, be very careful about putting excess stress/strain on your joints, especially your finger joints and elbow joints. Those tends to be the easiest to mess up, in my experience. I would advise against trying to do anything excessively strenuous until ~1/2 a year of climbing consistently (2-3 times a week). Until then, focus on climbing while trying to keep your center of mass as stable as possible, particularly when moving from one hold to another. Very few typical V0-V2 routes require a lot of dynamic movement to reach the next hold if the proper technique is applied to the move.

Another thing to focus on is reading your route and executing it. If you’re physically fit, there’s a tendency to just muscle through the lower graded routes since you can without applying the techniques to do the route without using the techniques that the setter was putting in the intended beta. If you’re stuck on the V3 plateau (which is reaaally common, so don’t get discouraged!), try doing the routes you can do using as little effort/strength as you can and try to force yourself to use those intended techniques. It will help you become more aware of the toolset available to you in particular situations and work out the muscles necessary to execute those techniques that are actually required for being able to send more difficult, complex routes.