Dr. Greene's Answer
Your question shows your thoughtful and observant approach to your son’s illness. Your reasons for doubting roseola are sound. Measles and German measles are also unlikely in 13-month-olds who were immunized against them at their 1st birthdays.
Rashes are still impossible to accurately diagnose without examining them. When the rash is accompanied by a fever and lasts as long as his has, it is wisest for him to be seen.
It could be a “garden variety” viral rash, but with his not eating or drinking much, I wonder about something going on in the throat. There are both viruses and bacteria that can cause throat infections with the symptoms you’ve described.
It is wise for children with a fever and a sore throat to be seen in case there is specific treatment that they need.