It sounds like a blockage. You need to trace the pipework to find where that might be. If it is an old house, the bath and sink outflows often join together and go through a single pipe out to a trap outdoors. Check that the bottom of the pipe in the trap isn't blocked. It could also be 'gunk' in the pipes, for which you can try those drain unblocker liquids - you probably need to unblock both the sink and the bath with them.