I know in at least four states that if you are a felon you can not work in anything that has to do with medical. One of my family member did something over 25 years ago and when she was a teenager when her background check came back they let her go and she worked in the kitchen at a nursing home she was told that any one with a felony can not work in the medical field. Check with the state that you reside in. These are the states I know that will not let you work is Indiana, Ohio, Arizona and Oklahoma.
FYI yes you can get your cosmetology license being a convicted felon. Each case may be reviewed by the board but the answer is definitaly yes.