Do not put Neosporin on that wound. Just as it is not meant for open wounds on humans, it should not be used on wounds that extensive on animals without a recommendation from a vet who has seen the wound first hand. Both the arm and the spots are related to the wound, and correct care needs to be given if you want to give the frog a decent shot. First of all, prepare a sterile hospital tank, with a sterile water dish (of course with treated water) and a paper towel bottom. Keep the towels moist, but far from sopping wet. I would also put in a few clean clippings from and artificial plant or some other suitable hide spot that can be removed and cleaned. This tank needs to be kept as immaculate as possible, so change the towels at least once a day, and immediately when soiled. Place it in a warm area of your house, but resist the urge to place it on a heating pad or some other device. Keep it quiet, and try not to disturb it too much. You need to contact a vet who is willing to work with you to possibly prescribe some antibiotics, if the arm is not broken, the swelling is due to infection. Most vets who have never treated an amphib or herp before still love the opportunity to learn, and you should be able to find someone who will work with you. Steer clear of anyone who suggests "lancing" the leg, force feeding at this point, or force feeding water with a syringe. I suggest making that trip as soon as possible. The spots that you see can also be linked directly with the frogs health, if they spread out or your frog develops an all over mottled color, then you have a whole new set of issues to deal with. I do wish you luck, and would love to be kept updated on your frogs progress. Just remember that everything you hear, from pet stores and even vets, is far from gospel, and you are bound to hear some crazy stuff, such as putting Neosporin on a wound that extensive without consulting a vet first. Antibacterial ointment can be used on amphibs, as long as it is the regular, non-pain relieving type. But some common sense should also be used, which you have obviously since you questioned it when the pet store recommended it. Good luck to you both.
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*~~Whitney~~*
Though here at journey's end I lie in darkness buried deep, beyond all towers strong and high, beyond all mountains steep, above all shadows rides the Sun and Stars forever dwell: I will not say the Day is done, nor bid the Stars farewell."