Minocycline and doxycycline are quite similar in their actions and side effects since both belong to the same group of antibiotics called tetracyclines. If minocycline has become ineffective there is no point in giving doxycycline. Other antibiotics such as erythromycin - which belongs to a different group - should be tried.
Low dose antibiotics can be given for a few months but not years due to side effects and resistance that develops in the causative bacteria Propionibacterium acnes.
Antibiotics do not address other factors such as trapped sebum in the hair follicles. Topical vitamin A (retinoids) helps unclog pores to clear up moderate to severe acne. Therefore in severe and resistant cases we use topical retinoids such as tretinoin and adapelene.
Sometimes acne is a manifestation of underlying disease such as Polycystic Ovarian Syndrome (PCOS); hence a consultation with a good gynaecologist is desirable.
Anti-androgens such as cyproterone acetate plus oestrogen can also be used in females.
A good dermatologist should be able to help your daughter in consultation with a gynaecologist to exclude PCOS.