Your question doesn't clearly state the reason why your doctor prescribed the injections. I'm aware of two possibilities: one could be a particularly bad infection that you have, and the second could be in case your cat has rabies, since rabies is so common in India.
If you have an infection
Infections from cat bites are pretty common and if not treated quickly can land you in serious trouble. However, they are generally treatable!
When you first get the bite, you should cleanse the wound in an antiseptic solution (I don't know what is available to you in India) or soap and hot water. Since cat bites are commonly puncture wounds, you should massage the area to make sure that the antiseptic is able to penetrate deeply into the wound.
Every few hours, repeat this washing and massaging procedure. Since this is a puncture wound, you do not want the skin to the "top" to heal before the "bottom" of the wound (the part in your hand) so keep massaging it. You can also soak the wound in clean (boiled) water if it's at a location that is convenient (I've gotten most of my cat bites in my hands, so it's easy to soak).
If your doctor is concerned about rabies
It's common practice in India to treat ANY dog or cat bite as a potential rabies source (source). The animals cannot be tested for rabies without killing them, but if the animal does have rabies and the person is not treated immediately it can be fatal. The doctors would rather give you injections that you don't need than have you die.
FORTUNATELY, there's a simple way to never have to worry about this concern with your cat! You don't have to abandon your cat, you just need to take her to a veterinarian and get a rabies vaccine. As long as you keep the vaccine current (get it redone following your veterinarian's instructions, which can vary from 1-3 years), your cat cannot get rabies and cannot pass it along to you.
Without more details, we can't really begin to offer suggestions about why your cat bit you or how to prevent it happening again. Most of my bites have happened when I was handling my cat too rough (usually when trying to give her medicine) and I accepted that she was using the language she has to tell me to back off. Learn the to understand the cat's language (ear position, tail position, whisker position) and you'll be able to avoid bites because she will tell you to leave her alone by lashing her tail or laying her ears back BEFORE she bites.