[jjl3rd]

You've got two separate problems. Water presure will not affect the drainage. You have to clean out the drain line. Get a more flexible snake.

The water pressure problem, if you did not have one before the faucet was changed is either inside the faucet or the shut off was not fully reopened. After replacing a faucet you should check the screen in the faucet head 'cause you just filled it with sediment from your work.