I have anemia and so I sometimes have a low tolerance to cold
Maybe you should see your doctor and ask for a complete blood count test.
I Hope you feel better.
You should go to the doctor so that he take blood tests to check out what the problem may be.
You may still have a virus or a bacterial infection if you have a fever.
When someone is very cold even when the weather is hot, this could be an underactive thyroid.
If the doctor prescribed you with the prednisone, you need to go back to him and tell him of your cold shivery feelings.
One of the side effects of prednisone is having chills. So it sounds like you may be having an adverse effect from the prednisone.
To help relieve the congestion of your sinus problems you can do steam inhalations, by getting a hot bowl of water with vick or olbas oil and breath in the steam with your head over the bowl covered by a towel. Be careful not to scald yourself.
Rather than the prednisone, you may be better off having an antibiotic prescribed by your doctor if your sinus infection is caused by a bacteria.
If it because you have an allergy, you may benefit from antihistamines or simple nasal sprays (don't use these long term because they can damage the nasal lining).
It appears to me that you are having these constant chills because of the prednisone, that is why you need to see your doctor.