Some shower/tub control valves and even sink single-handle valves can develop a cross-over. This can provide a short-circuit to either hot or cold water...it's usually the hot since it has more restrictions through the water heater - the cold wins and flows through. When this happens, shut off the supply to the sinks or ensure that the control is set to the full-hot or full-cold side (if possible) and see if it clears up. If you find the offending valve, replace the cartridge. This assumes you get flow, but no hot. If the flow shuts off, that's another thing altogether.