We are sorry to hear of your accident and wish you a refuah sheleimah.
A plaster cast cannot get wet and constitutes a chatzitzah. Unfortunately, in the situation as described, you would remain niddah until after the cast is removed.
If you haven't yet, please consult your physician about the possibility of removing the cast briefly and using a removable splint so that you can immerse. (In this type of case, it would be permissible to immerse during the day from the eighth day onward.)
It is worth noting that sometimes casts are switched after a few weeks for medical reasons. Plaster casts are also often replaced by fiberglass casts to allow people to swim, and thus asking for such a change is not unreasonable. These changes may be able to be coordinated with immersion.
Please write back with any follow up information.