Tried to tighten hot water tap to stop a drip and

Make sure the water is isolated and take out the taps centre with the washer on on the bottom end they should be a little circlip halfway down the valve body it sometimes jumps out the little groove stopping the valve from working the valve body will scew in anti clockwise screw it together fully then re apply the little clip

There is normally a plastic washer at the end of the valve stem which you turn to allow the water to flow and to stop the flow. It sounds like this washer has either deteriorated or been damaged by over-tightening. You will need to remove the stem and replace this washer. It is normally held in place with a screw.

You will need to remove the on-off handle and probably a stem cover to access the flats on the stem where you can place a wrench. These flats will likely be recessed into the shower wall; therefore, it will likely require a deep socket to reach them. Most hardware stores will have the sockets needed to remove and replace these stems.

Of course, make sure that the main house shutoff valve is closed before you start to do this.