Puppy paw closed in door

I'm sorry I haven't been posting on other threads - it's been so busy with Tenzin.

Last night I took him out to go potty before bed, the door was open, but I thought Jofi was upstairs, behind the gate in the kitchen. Suddenly she came rushing down and I quickly went to close the front door. I didn't realise Tenzin had one of his front paws on the door step - near the hinge. He screamed for about 20 seconds. We inspected his paw carefully - pad, nails - there was no blood and nothing feels different than the other leg, also he made no reaction when we touched it, but since it happened he's got a limp. When he stands, he holds up the affected leg. It was about 1am last night when it happened so we put him in his crate to sleep and see if it was better this morning. It's now 7am and he's limping still - if anything it's more pronounced. We're going to take him to the vets as soon as possible - probably in a couple of hours (he slept through the night without making a sound). I feel like such a bad mummy - I really hope it's nothing too serious.