Hello,
For hair on chin, you can get shaving, waxing or epilation done. try to wax the hair out in a single strip as multiple strips may injure the skin more. After waxing apply ice(wrapped in a towel) and some calamine lotion on the skin which helps in soothing. You can also take some over the counter anti-inflammatory like ibuprofen after waxing.
However,the best method of painless hair removal is by laser treatment. I would advise you to consult a dermatologist/cosmetologist and discuss this option with him.
I hope it helps. Take care and regards.