Thanks for the additional information.
I do think the cause for his shivering is pain or discomfort. I wasn't thinking he was cold but I had to ask...you never know. Some people keep their dogs outdoors!! :)
You probably also know that doxies are very prone to back problems. Disc disease can certainly be intermittently painful, especially early in the process. If the mattress doesn't provide a lot of support or if he sleeps in one position too long, he may become very painful. This would explain his reluctance to move. He is at the right age to be experiencing some degenerative back problems.
Gastroenteritis can also be painful (cramping, etc) and may explain the licking which can indicate nausea, however, I would expect symptoms such as a decline in appetite, vomiting, or diarrhea.
The licking can also indicate nervousness, which would be expected if he were in pain.
If he sleeps in a different spot during the day, I would focus on some type of pain, likely from his back just given his breed. A complete exam including spinal compression, can sometimes confirm this. Sometimes an MRI or contrast study of the spinal cord is needed. I would recommend you have him checked as anti-inflammatory medicines can provide a lot of pain relief and will stop the swelling from progressing (at least to a point).
Let me know if you have any other questions. Have a great day!