How long has it been since the frog has eaten? Does it look like it is losing weight? If it's been over a week, you may want to do an 'aggravated' feeding. If he won't take prey on his own, you can rub the prey over the frogs lips and chin for a few minutes. Usually they will get annoyed and bite it. This is less stressful than actually force-feeding.
Post some more pictures of the bite area and the whole frog please.

When you say he is 'gulping' water do you mean he is sitting in his water dish and opening his mouth over and over? If this is something you've only seen him do once, he may have just been shedding in the water dish. They gulp air to puff up and loosen the skin.

Sitting with the eyes closed all the time isn't a good sign. You can try feeling VERY gently around the bite area. Do you feel any hard knots or swelling? Without a picture this is just a guess, but sometimes a wound can heal up and leave a sort of encysted infection under the skin. I've seen this in other animals (especially cats) that receive bite wounds that don't get immediately cleaned out. This can either lead to another infection in the same area (the pus trying to escape and reopening the wound), or the infection going through the body.

Is there an exotics vet you can get to? If the infection is spreading beyond just the bite this may be beyond what you can treat at home. With infections, the sooner you can get them treated the better.