There are other options you can explore - polyurethane or tactylon condoms (non-latex, both of them), female condoms (they're all non-latex), copper-T IUD (VERY effective), spermicides.
Does your problem with hormonal BC concern estrogen or estrogen AND progesterone? If only estrogen then there may be a hormonal solution with BC methods that contain only progesterone (minipill, the shot, etc.).
By the way, while your bf is demanding plans and backups for your contraception you might ask him what he is doing to find information on it ... Contraception concerns both of you. You might like to point out to him that a vasectomy would be very effective and would not have adverse effects on your health View Thread
Yes, it will work as birth control. The only thing that changes is that you are missing inactive pills. As the inactive pills don't actually do anything and it's the active pills that do you'll be fine. OTOH, sometimes you get breakthrough bleeding when you take your pills like that - i.e. your period doesn't completely disappear each month - so don't be surprised if you have a little spotting View Thread
You start your next pack of pills when you normally would - finish your third week of pills, take your week off and then start your next pack. When you have your period does not change the routine of your pills. Be sure to use backup contraception for two weeks.View Thread