Yes, of course: UV photography is used in forensics and 'bee view' flower photography, for example. Humans are trichromates and so are bees. But they see UV and do not see red. Some flowers look totally different to bees than to us.
For the fun part: It would not be a problem to make a camera to see if sunbathing people use an efficient sun blocker and if they applied it to the whole skin or if some parts are missing.
Can you just get filters for normal webcams to only allow IR or do you need a special camera?