hi:) infections are a common side effect with mirena users - some people are more prone to them than others, and it sounds like your system is not coping well on that side of things. Obviously taking Antibiotics all the time is not a long term healthy option but nor is living with infection down there, so for that reason alone, i would get the mirena out. No doubt you are taking pro-biotics to help get your gut bacteria up and running again after the Antibiotics . If so, carry on with those, and any natural, plain live yoghurt is good too - only to be taken on an empty stomach though, and not mixed with fruit, just plain!!
The hair loss is distressing and another sign that your body is not taking too well to having it's hormones messed with. But the migraines are a serious risk to long term health because the blood vessels can constrict which obviously raises stroke risk etc. Stress can also have an effect on the hormone system. The more stressed we are, the more out of balance our hormones get, so it is important to do some kind of relaxation technique that suits you, as well as NOT stress the adrenal system - ie, no caffeine, cut down on Sugar and alchohol, if you havent already. Unfortunately when you are having these kind of problems, they tend to get worse the longer the mirena is in. the only way to heal your body is to get it out, to avoid any more synthetic hormones, in order to give your body time to recover.
This is your decision, and i can only speak from my own experience and that of others on here and research i have done into the subject. All that i have learned so far, suggests to me that your body is telling you that it is not happy!! Getting mirena removed is only the first step, but a positive one none the less. If you go to the links i will post at the bottom of the message for you, you can read more information on mirena for yourself.
good luck, and please let us know how you get on:) thinking of you:) x