If your cat has been scratching and you have been getting bites and itching bumps, seems that the cat may have fleas.
Treat your cat for fleas. Strip all your bedding and wash it on the highest wash. Vacuum thoroughly. Vacuum the mattress, under the bed, every nook and cranny. If you have soft toys, wash these. If you are not able to wash any soft toys, put them into a freezer bag and pop them into the freezer for a few hours or overnight.
Bed bugs are very small and they can bite too. Vacuuming and cleaning everything will help.
For the itchy rash, you can use antihistamine medication to take by mouth. If the doctor has not given you anything to ease the discomfort on the skin, you can purchase a calomine based cream or lotion from the pharmacy. Applying natural set yogurt to you washed and gently dried skin will also help to cool off the hot itch. As hard as it may seem, try not to scratch. Scratching can cause broken skin that will allow bacteria to enter and can cause infections.
I suggest you see a different doctor next time.