There is a thin white/clear coating on my tongue, as well as red bumps in the far back. what could this be?

White Tongue: A white coating on the tongue is usually the result of irritation of the taste buds, or papillae, caused by debris, bacteria or dead cells on the surface of your tongue. The condition is not serious. However, a white tongue can also be the result of a yeast infection. See your local doctor for a diagnosis.

Sounds Normal: The coating is very common and is made of saliva, bacteria and food debris. Try brushing with a dedicated 'tongue brush' or tongue scraper appliance from your drugstore. Scrape from the back of your tongue, forward, then rinse the scraper. The reddish bumps are large taste buds called papilla at the back part of the tongue. All normal.

More info: My colleagues already gave you excellent answers regarding your symptoms. If the coating goes away after a week of using a tongue scraper (or tooth brush) daily, there is no concern and you should continue to do this on a regular basis. If the coating remains, it could be several things and should be evaluated by your dentist.