Teething?

My baby just turned 3 months today. Sunday night she started to feel warmer than normal and was up every 2 hours to feed, normally she will give us at least one 4 hour stretch. Yesterday morning she still felt warm and we checked her temp - 99.0 under her arm and 99.3 rectal. Technically not a fever, but definitely elevated from her baseline. Later in the evening she started to get harder and harder to console when crying, increased drooling, not latching well/not eating a lot and was shoving her hands in her mouth a lot more. We decided to give her some Tylenol and about an hour later finally fell asleep for her normal 4 hour stretch at night. We noticed this rash this morning. It doesn't seem to hurt her at all- but it is on her neck, back and belly. I called the doctor's office this morning and the nurse said she's too young to be teething. She is still smiling and acting normal for the most part. Just has some bouts of crying where nothing works. Curious to see how tonight goes. Has anyone else experienced this?