Can't say it enough... footwork. Focus on precise footwork and quiet, controlled movement. Doing a lot of traversing is a good way to work on footwork, slabs too. You can also play games like Sticky Feet (when you place a foot you can't move or adjust it until moving to the next hold). There are more footwork drills a Google or Youtube search away.
Rest is just as important as trying hard. If you try to progress through grades too quickly you're going to get injured. Work on doing problems, that personally feel moderate, perfectly. So you're bouldering at a V3-4 level, do all of the V2s on a certain wall perfectly next time before pulling onto anything 3+. Keep doing that until you can do all of the 3s on that wall perfectly before climbing 4+ and so on.
I know it's hard, but don't worry about the grades, they will come when they do. Concentrate on staying healthy and building tendon strength. You can start doing fingerboard, aka hangboard, exercises once a week to start out, but I wouldn't do it any more than that at first. I could go on for a long time about all of this, if you have any questions you can PM me. Here's is a nice little template to start out with:
http://www.metoliusclimbing.com/training_giude_10_min.html
Try hard and stay motivated.