Your rabbit most likely has snuffles and will need to go to the vet and get some antibiotics. Here are some vet listing for good rabbit vets. This in not caused by molting, and the people most likely knew they were giving you a sick rabbit.
http://www.rabbitsonline.net/f28/finding-vet-13366/
http://www.rabbit.org/vets/vets.html
If your rabbit is nervous being in a new place, I would leave him alone as much as possible for a few days, aside from seeing a vet, and not wipe his nose, it will be ok for now. You don't want to overly stress him as too much stress can make a rabbit sick. If he seems friendly and interested in you, you could try lightly wetting the nose(you don't want him breathing in any water), and let it sit for a few minutes, then try lightly wiping with a warm damp cloth.
Just a few things about having a new rabbit. Rabbits can get really sick with sudden diet changes. Hold off on the rabbit pellets for now and feed unlimited timothy hay. Rabbits need to be slowly transitioned onto new foods. You can start the rabbit pellets, but start with a very small amount like 1/2 teaspoon morning and night, then gradually increase that amount over 2 weeks time til you are up to a normal amount. Recommended amounts for pellets are 1/4-1/2 cup pellets each day per 6 lb body weight. It's best to split it up into a morning and night feeding. Also make sure he's drinking water and if he has a water bottle, make sure it is working ok. Make sure to also use a rabbit safe litter like pine pellets, newspaper pellets, aspen bedding, carefresh, or kaytee soft granule bedding. Don't use cat litter, pine shavings or cedar shavings. They are all bad for rabbits. I would recommend checking out the library section on this forum, to learn about the care of rabbits. It can help you avoid common mistakes often made with new rabbit owners. The house rabbit society website also has good info. Here are some veggie lists as well, and the proper way to introduce new veggies. You only want to introduce one new food at a time, including pellets, so that if the food causes a problem, you will know what caused it. Keep an eye out for any changes in the poops. There are normal sized round fecal poops and grape cluster like cecal poops. Extra small poops, irregular shaped poops, and soft mushy ones, are a sign of a digestive problem.
http://www.rabbit.org/care/veggies.html
http://www.3bunnies.org/feeding.htm#greens
Good luck! I hope your poor little guy is going to be ok,