It is indeed hard to find a vet that knows rodents, though it's worth a try.
Unfortunately the best route, assuming the vet doesn't know anything about them, is to ask either a breeder or a pet store that specializes in rodents.
You could have a few problems.
Mites - Have you seen any tiny black specs? There are also mites that aren't visible to the naked eye, so if no specs are present he could still have them.
Bedding - What do you use? Mice and rats can be EXTREMELY sensitive to wood litter. Some woods are likely to cause respiratory or liver problems, and even the ones that supposedly don't will if not changed enough. ALL wood will irritate the skin in some rodents. There is also a chance that certain wood shavings will repeatedly reinfect your mouse with mites, so it's best to use a compressed paper bedding. Try to find bedding that contains no dye since some dyes can irritate the skin of rodents, especially mice and rats since they tend to burrow and bed down in the litter.
Housing - Is he housed in a tank or cage? Tanks are a bad idea for mice and rats because they're hard to keep completely clean and irritating fumes and other substances build up and harm your rodents lungs and skin.
Food -
This is the most likely problem does it have any dyes in it? Rats and mice can have allergic reactions to certain dyes.
What kind of mix is it? Male mice especially seem to develop an intolerence to mixed foods, ESPECIALLY if they're a hampster mix, not especially formulated for mice. If the food you feed is not SPECIFICALLY for either mice or rats, I would not feed it.
Assuming your food IS formulated for mice, it may not be as balanced as you think. Mice usually pick out all the fattiest and tastiest parts first, and some mixes formulated specifically for mice aren't balanced anyway, whether they appear so or not. A high fat diet, or a diet consisting of the wrong type of grains will definately cause scabs and sores on your mouse, this is quite common.
The best diet for a mouse (besides homeade) is lab blocks specifically for mice and rats. Yes, lab blocks are boring, but I would try your mouse on them for awhile and see if his sores go away. You can supplement with a tiny bit of veggies(such as carrot and raw peas) and acceptable grains. The main source of the diet should be lab blocks though. Meal worms are also a good source of protein and nutrition when fed as a treat every once in awhile.
Rice, oats and barely are all acceptable grains. Millet and Sunflower seeds can be fed after your mice recovers and there is no more itching or swollen eyes. If symptoms show up again I would stop feeding them.
Don't feed peanuts because they're way too high in fat. Onion and Chocolate is toxic to mice just like cats and dogs. Sugary treats are always bad.
This site has quite a bit of info on diet:
http://www.rmca.org/Resources/mouse-faq.txt
(Section 3 is dedicated to diet. 3.08 talks about itchiness, sores and hotspots as related to diet)