The drinking and wetting at the same time does sound suspicious. A UTI check would be a good idea.
It can take a while for the bladder muscles to develop completely, but at 17 weeks he should be getting close to full control.
He hasn't been neutered yet, has he? I would worry about a surgery slip, if that was the case.
If you leave him contained in his crate (or sleeping space) - can he hold it?
If so, I'd work for 3-4 days on spending a LOT of time in the crate (~2 hours at a time), to make sure he exercises the bladder "hold it" muscles during the day. That would also help get him on a schedule, and maybe promote full emptying when he does go out.
I'd put him on a routine with absolutely no unsupervised time in the house - that's where the house-leash comes in handy - keep him tied to you at all times, so you can learn his 'cues' to go outside - and also correct with a firm "no" if he does start to go inside... with a quick scoop up and outside (can he stop the stream once started? i.e. when you pick him up?) - once he finished outside, a big Potty Party and rewards (we play fetch & tug as rewards outside) before going back inside... give him a good 10 minutes to decide if he needs to go again or not. Boys are notorious for not finishing... they always need to have some reserves for marking the next bush.
If you can 'name' the event ("potty" or "get busy") that will help him learn it, too. When he starts to pee in the appropriate location, start chanting your 'cue' word (potty, potty, potty), and stop just before the stream does. Once he gets the idea that "potty" and going pee occur together every time, you can start to ask for a "go potty", and he'll hopefully connect the two (Pavlovian response). This is a very helpful command for times away from home when he doesn't want to go on a strange surface (gravel versus grass), or needs to find the perfect tree or bush to pee on...
I'd double the recommendation for the "simple solution" or "natures miracle" enzymatic cleaners. They helped us keep carpet and rugs from smelling like a toilet around here - although cat pee still seems to be too strong if allowed to dry before application...