The night I got my silicone cohesive gel implants removed, I had such bad fever and chills I couldn't sleep. Is this normal?

This is not normal part of the procedure.  Usually there is a physician who is covering a doctor if a doctor is not available or out of town.At times low fevers can be from the lung, something we call atelectasis.  Due to the anesthesia and the surgery, the patient not breathing deep enough can cause collapse of small parts of the lungs leading to fever after surgery.  Obviously the major concern would be a surgical site infection when you are not feeling well and having fevers.If you are not able to get in touch with your surgeon, then the next best coarse of action is emergency room visit.Good luck.

It is important to reach out to your surgeon to discuss your symptoms. Fever could indicate an infection. Your surgeon should have an answering service or some way of contacting him in case of an emergency despite the office being closed.

I would advise that you call your surgeon's office as soon as they open in the morning.  If your surgeon is out of town, there should always be someone covering for his patients.  If you are continuing to feel sick with fevers and chills, and you are not able to get a hold of your surgeon, then I would recommend going to the nearest Urgent Care center or Emergency Department to be evaluated.  Some of the things you described are concerning and need medical attention.  

There should be a way for you to communicate with the surgeon directly or whomever is on call for the practice to answer questions. 

Persistent fevers after implant removal are concerning. I would follow up with you surgeon as soon as possible.