10 minutes without any advice, that's horrendous!
I remember doing 6 mins once and had a very sore tummy after. Never used them much (had a friend who working in a tanning salon so went on in there a few times) and don't use them anymore especially as on medication which makes my skin more susceptible (worth checking if you're on any).
3 mins is more than enough for a first time and it should be worked up gradually.
Goggles should be worn as it can damage your eyes. Also, contacts should not be worn.
A good aftersun lotion would help, Banana Boat do a lovely cooling Aloe Vera gel one.
You will need to make sure that you keep the damaged skin away from the sun to avoid further damage to that already done. It can make you skin horribly dry as well so a good gentle intentive soothing moisturiser would be a wise investment. Avoid anything perfumed and full of chemicals.
Definitely take it up with the local authority. What they are doing (or rather not doing) is down right dangerous.