If the sink sprayer has pressure, water is getting to the sink, through the sink valves, and to the redirection valve... so the question would be why it isn't getting to the main tap. Presumably something is blocking/plugging that path. If removing the aerator doesn't solve the problem (in which case you need to replace that aerator), and you're sure the tap has in fact been hooked up (check underneath; some snap-on connection systems may be self-sealing if left unconnected), the only thought I've got would be to disassemble and see if you can find the blockage.
Shower head: Is there also a tub spout, and does it work? What happens when you remove the head again and just try to run water through the pipe? Are you sure you haven't thrown the "stop water while I soap" valve?