First of all, congratulations on the new little gerbil.
Ok, if it's been 2 weeks since he broke his limb, he should be almost healed by now. Second, his nose could get worse in that cage, since they usually chew the bars of the cage, and lose the hair on his nose that way. I've had a couple of compulsive chewers, who chew everything in sight and lose their nose and cheeks hair. Doesn't seem to be passed on by generations, though...just their personalities. Then, check that he's not having allergy to the bedding. Try by changing his bedding to unscented, uncolored toilet paper (or paper towels) to see if he stops scratching.
Still, I suggest that you get him a companion, as they are very social animals. The prefered method to put 2 gerbils together is the split cage method, in which you put a wire mesh division in a cage, and put a gerbil in each side, so that they can see and smell each other, but can't fight through it. It words pretty well with males, females or male/female pair, but works better if one or both of them are still pups (5/6 week old pup). You have to switch them from side every couple of hours so that they get used to each other's smell and after at least a week, put them together in a neutral environment and clean very very well their cage before you put them. Sometimes with males and very young pups, you can put them together in neutral environment and they can get along, but it's a risk, and you have to watch them very very closely for a long time.
Good luck with them. 8)