I have broken blood vessel inside my eye and it is affecting my vision. What is the diagnosis and lenght of cure?

Depends. When you say inside of your eye, this is hard to assess as there are many structures in the eye that can have bleeding in such as sclera, anterior chamber, vitreous, retina etc. If you know which one you have bleeding in, you need to let us know for us to be able to help. If you don't, then you needs to be promptly evaluated by physician.
Retina bleed? If you say "inside my eye" to me it means a dr. Saw your retina with an ophthalmoscope or a sort of magnification and maybe dilated your pupil to see better. If that is the case you need an ophthalmologist or retina specialist that treat this. By "broken vessel" may mean "retina bleeding" or "retinal infarct". You have to ask the person who examined you. If u have not seen a dr. Go ahead.