A couple of things…First, charting your fertility signs should be step ONE in determining fertility problems. Seriously, try to track down ANY NFP teacher in the UK (I simply can’t believe that there are none) and start learning about how to track your signs. Simply looking at a woman’s chart can show a doctor (who knows what he’s looking at!) so much. .
So, in fairness to the OP, people without dysmenoreah (irregular periods) should really not offer advice here. I have PCOS. I tried charting my “fertility” for 6 months and the problem when you don’t have periods is that you are basically not fertile. So the charts tell you absolutely nothing, and are very frustrating.
Second, I’m not sure how horrible your periods are (you say you’ve been hospitalized for the pain?

Ouch!), but my wedding day was Day 1 of my period and it wasn’t so bad.
Seriously, I usually feel the cramps down to my knees, but somehow power-loading advil, in combination with the adrenaline and excitement of the day, took my mind off the pain…
Again, the OP is talking about her, and her periods, not you and yours. When you don’t have a period for 6 months, the one you do have is huge, painful, impossible to control with tampons and pads together, even changing every 15 minutes. And, the pain is unbearable (ovary pain, back pain, leg and muscle pain) and you are exhausted.
Finally, I would never take any “magical” pill from a doctor that is supposed to change my body’s natural system to do exactly what I want it to do. Your fertility is a fragile thing, and toying with it like we modern women tend to do with our hormone pills and patches and such is really like playing with fire. (I’m not trying to be scary here–just honest. Most BC pills have had fatal side effects at least once or twice, and hormone replacement therapy doesn’t have such a great reputation, either.) I’m sure there are hormones involved, and hormones inevitably affect a) natural fertility, and b) every other bodily system. It’s just not something to mess around with, and can have long-term consequences.
Not trying to be scary
OP, please find a good endocrynologist. From what you say, it sounds like you have PCOS. I have PCOS. Interestingly enough, the only time I get my periods is when I go on vacation, or have an important life event (yes, I did get my period on my honeymoon
If you have PCOS, you maybe(are probably) infertile anyway. The pill may actually be exactly what you need to regulate the hormones in your body to help you be more fertile in the future.
I am no doctor, and can not offer you medical advice (but neither are the other posters). I understand and empathize with your dilema. I suggest you discuss this first with an endocrinologist to understand your fertility, and then with a priest. But I would guess, since the chances are you are not fertile, and taking hormone pills for a period of a year or so may actually improve your fertility, your priest may say its OK.