Hi,
Thanks for posting in HCM.
Well, broken or cut blood vessel on finger cannot be ignored. You need to visit emergency room at the earliest to get it treated. Till then, apply a tight bandage to arrest bleeding as much as possible.
Since it is at the joint, you may require an x-ray to know the extent of involvement of joint. Depending on the extent of
injury, it may require cleaning and suturing of wound. It will be done under
local anesthesia under aseptic conditions. The joint may be immobilized till the wound heals.
You will be also administered a dose of tetnus toxoid injection,
analgesic and antibiotic medications. After a week, you need to get your sutures removed.
Keep the wound clean and dry so that it will not become infected, as infection would delay the healing process.
Hope the information provided would be useful.
Wish you speedy recovery.