My dentist prescribed a night guard recently and now that I wear it, I have had ear stuffiness, jaw, neck, and throat pain. There was no pain before using the guard. What should I do?

Try this. Try to go without wearing the appliance for a couple of nights, if your symptoms remain == contact an otolaryngologist (ear, nose ; throat physician), then it is probably not related to the guard. If they go away, contact your dentist and bring in the guard to have it evaluated.
You have a TMJ Issue. Try to find a neuromuscular dentist in your area and have him/ her help you with your TMJ joint issues.
Stop using guard. I agree with dr. Gordon. Try not using the nightguard for a few days (5-7 days) to see if there is any resolution. If it does not improve, you may consider seeing an ENT or a dentist familiar with TMJ conditions. It is possible that wearing a guard precipitated an underlying condition that was already present. Why was the guard prescribed in the first place? Did it serve that purpose? See your dr.
Something is wrong. Night guards are prescribed to help most of those problems. These devices need monitoring and adjustments to work properly. Let your dentist know as soon as possible and take your appliance in when you see him or her.