All lamps that have a fixture which would be capable of emitting UV lights (mostly HMI lamps) must have UV filters in front of them. Typically they are part of the fresnel lense. For LED this is a non-issue.
If you got a sunburn in a studio, that means they either used shit lamps (non-industry standard), or the filters have been removed. Either way this is a work safety violation and any study worth their salt wouldn't stand for it.
The lamps are of course still something that you need to treat carefully. First because it is a ton of power and heat, but also because they are heavy. But if you use them in the way intended by the manufacturer they are not more dangerous than anything else.
A typical Arri HMI will even have a diagram with safe distances for heat radiation engraved somewhere on the body of the lamp. So you don't even need a manual to know you are doing it wrong.
I once had a HMI with a broken lense through which UV radiation would leak on a outdoor set. We noticed this because a fist-sized pile of insects started to accumulate right at the spot where the leak was. The smoke from that was quickly noticed.