As you are appearing again , you are suppose to pass the exams in order to be called as eligible for further studies .So focus on your studies and you are supose to clear this time.I know you are going to do wonders.

Yes you are eligible but you'll be considered in the division of people appearing for the exams once again. On medical grounds also you'll have to pass the exam in order to pass class 12th. Also there will be an *improvement* printed on your report card as you have given the exam again.
Hope this helps
All the best for exams.