Firstly by what you are saying it sounds as though you are getting insulin residence when you BG’s are raised, the higher you BG the higher the ratio of insulin required, i.e. a normal correction could be 1 unit will bring you down by 3mmol/l, but above a certain BG you could need 2 units of insulin to being you down by 3mmol/l
It also sounds as though hormones are playing apart in your control; however is this a direct link to the Pill or whether this is being caused by a normal monthly hormone cycle is hard to say… A lot of women do find that there insulin needs will change during the month…
You need to ask yourself, have I changed the type of Pill recently, if so has these changes happened since I changed? If the answer is yes it is highly likely that the pill is the main cause of your problems…
If no, then you’re have to look at what is happening during your month cycle to see if there is any set patterns which you might be able to adjust to gain better control.
As to the Pill, it might be worth talking to your GP concerning this, as different Pills having different levels and composition of hormones to prevent ovulation in a female, so changing brands or type , might work much better with your natural hormone make up