Get that hand seen to, my mate. You may have tiny pieces of glass in there and the last thing you need is an infection. Some house glass can be seen on X-ray, depending on the angle of the fragment relative to the beam, so an X-ray is in order. Just tell the A&E people that you tripped and put your hand through house glass. You get the rays, the stitches, home the same day (maybe with antibiotics). End of story.