First of all welcome Skib, sorry about your knuckle. One of the first tings I would do is apply a drop of Krazy Glue to the broken off part and stick it to the part still left in the bottle. Next use a little warm oil around the opening but also wrap a very hot wet cloth around the whole top of the bottle and cap. This should help to loosen it up.
One thing to remember for future reference is, do all of theses things first (except Krazy Glue), and always wrap a cloth around the stopper and very gently work it, if it does not budge try a little alcohol, then do the oil.
Good luck, and if you ever want to share/ trade a small sample of your treasure (once it is opened) please know I would be thrilled.