Hi. Welcome. My name is***** I'm sorry to hear about this situation with your guy. What is his name? How long ago was he last seen by your vet? That wet, sticky, moist fur sounds pretty suspicious for a hot spot (an area of moist dermatitis). If this is what is going on, ideally the fur in that area is shaved off to allow that skin to dry out and heal. If there is fur in the area, it traps moisture and the discharge and doesn't let it dry out well. If this fur isn't trimmed, it doesn't really have a chance to dry out. Antibiotics are utilized in these situations to help aide in the healing.
In a situation like this, one of the options that i'd throw out there is calling your vet to let them know what you're seeing. They may be comfortable in letting you bring in some video / pictures of what you're seeing and then doing a script of antibiotics based on that. This isn't something that all veterinarians can / will do. It is a case by case basis. They've already established a veterinary / client / patient relationship and that may allow them to do this if they feel comfortable. There really isn't any antibiotics that you can get on line to help with this.
Give your vet a call and see what they can help with. They have every best interest at heart for him. I'm hoping for the best!