The pill does not stop hell week, except in very rare cases. So I'd recommend trying to get back on T instead if you can find a way.
Oral contraceptives are generally taken for 21 days of the month, then you either stop taking them or use a placebo for seven days before starting them up again. During that seven-day break, most patients experience hell week... although it is generally lighter than usual. With some brands you could use two packs one after another without a break (i.e. 42 days) but then you
must stop taking them and you'll probably get a
hell of a hell week at that stage.
I used a progesterone-only pill because I wanted to avoid oestrogen, and I can tell you that it didn't stop my monthlies; it just made them lighter. I'd have about three days of light, painless bleeding instead of my usual five days of heavy, painful bleeding. The pills normally contain progestogen, which is a synthetic form of progesterone. Progesterone is the 'pregnancy' hormone so it can actually cause your body to respond as if it were pregnant. So yeah, that includes laying down extra fat, retaining water, and breast growth.
There are health risks attached to oral contraceptives (as there are for most medications). Many of them are not suitable if you have certain health conditions, such as heart disease or epilepsy, so you probably couldn't take them. They also interact with several medications.
There are other medications available that can reduce the severity of hell week. Here's a good resource giving you some ideas, but I'd imagine a lot of these things would be expensive on your side of the Pond:
http://www.nhs.uk/Conditions/Periods-heavy/Pages/Treatment.aspx There are also other contraceptive choices (such as the implant) but that takes about a
year to reduce the severity of hell week.
Whatever you do, this is a very complex issue so I'd recommend discussing this thoroughly with a doctor before making any decisions.
In the interests of full disclosure: I've done a lot of in-depth research into contraceptive pills, because the one my mother used for many years caused her to die of breast cancer aged 48.