From the description, I gather you primarily have two concerns
Waxing or threading induced folliculitis
or perifolliculitis- it can be treated by application of flutibact cream twice in a day and tretinoin
cream in night.
Hair growth- the hair growth over chin can be reduced by waxing followed by eflornithine
cream application daily
Though you are reluctant about laser
but it is the best treatment option in your case.
Hope that answers your query.