Any special restrictions after cortisone injection in the eye?

Monitor symptoms. Injections into the eye have a relatively low incidence of complications, but those complications can be severe. You should monitor for eye redness, pain, or vision changes in that eye until your scheduled follow-up. Make your ophthalmologist aware of any such changes immediately.
Yes. Follow all the instructions to the letter given to you by the ophthalmologist. You must be compliant to prevent serious problems.