as far as i'm aware, the only issue with 'bones' is if you take it whilst pregnant the baby could/ would develop with yellow/grey teeth. i've not read anything about long term use causing weak bones, i'd be very interested to know where your information comes from as i've been taking oxytetracline for about 15-20 years.
it may be that your son would benefit from a relatively short course - maybe 3-6 months - to settle his skin down. i very much doubt that 6 months of it would cause any problems, and may just do the trick for him.
i've tried every over the counter product known to man over the years and nothing has had any effect. if your son has a serious case of acne he needs specialist treatment.