Some great advice so far. Start off by thinking like water, BE water (a little bit of Zen fun). There could be a 1,000 causes of the problem: but you're only looking for one. Loose washers in faucets & taps (I'm English) will make plumbing whine, squeal, chatter, moan, vibrate, hammer & all kinds of other noises, which will or can be heard all over the house. That same loose washer, also restricts flow, maybe just enough to allow a shower, but when a shaver comes along, the shower washer closes & flow goes to shaver! I bet it's something very simple....wait till JES or Dale get here, they'll aim you in the right direction. You could install a tankless heater from me, just to feed the shower & plumbs into the cold water side, but you have cheaper options than that. Find what's causing the moaning & you'll probably fix the problem. There is a restriction of some kind (scale to that extent is dubious), so it's something mechanical, check washers & partially closed valves etc'. But DO let us know what you find, because you help us too, then we all learn. Good luck, Tankless Brian.