General interest in contraception. Girl does not wish for a combined pill due to the side effects. Is mirena a good choice without investigating what the reason is for irregular periods?
It is very common for young girls to have irregular menses. This hypothalamus-pituitary-ovary axis. After menarche, the interactions between these three organs is immature, which leads to irregular bleeding, which at times could be quite heavy. Oral contraceptives are usually a first-line treatment for this problem. However, remembering to take a pill every day can be quite difficult. And when pills are missed, there can be withdrawal bleeding (as well as less efficacy from a contraceptive standpoint).
Another method to consider would be the depomedroxyprogesterone acetate injection (called Depo Provera in the US). It is a progestin-only method of contraception that works by inhibition of ovulation and thinning of the endometrial lining. By thinning the lining, the bleeding pattern can be much improved. Side effects can be spotting (sometimes daily) for the first cycle of use. This method lasts 3 months and requires a return to the clinic for another shot every 3 months.
Finally, the most effective methods of contraception are long-acting reversible methods. In particular, I would recommend the levonorgestrel intrauterine device (Mirena). It has been shown to work well for heavy or painful menses. Also good evidence exists that it is well tolerated in young women who have not yet had a child.