Although it does sound like something that needs to be looked at by a vet, I just wanted to throw in a quick tidbit on how to clean up a dog's accidents, as it can actually prevent future accidents. You mentioned that you're following the pup around with a bucket of soapy water...what product are you using to clean up the pee and poop? I'm asking, because dogs will smell their territorial markings, and continually revisit the same areas to eliminate if the odor of their markings are still present. Check into a enzyme-based pet accident product, such as Nature's Miracle, or Simple Solution, and after cleaning up the actual pee and poop, treat the area with these products for quite a while to eliminate the odor...trust me, your dog can smell his accidents long after you can't! And my other recommendation, is to not allow him to witness you cleaning up after him...relocate him to a different area of your home, or place him outside during the cleaning.
Like I said before, it sounds like it could possibly be a UTI, which will need to be treated by a vet. These are common ailments in dogs, unfortunately, and I would be willing to bet that it won't cost you an arm and a leg in vet bills to solve the problem...
Good luck, and let us know how he's coming along!