3 month old w/ fever (no other symptoms)

My baby will be 3 months next week. She’s had a fever off and on for about 3-4 days now. I called her doctors office and was told that it’s probably just teething and to give her Tylenol and Motrin throughout the day and as long as her fever doesn’t get above 102 that she’s fine. I gave her tylenol about an hour ago and her fever was 99.6. I laid her down to sleep and she woke up fussy and felt hot again and her temperature went up to 101.2 in just that hour. She hasn’t had any other symptoms that I’ve noticed. She’s still been having the same amount of wet diapers but she hasn’t been taking as many bottles. The doctors office also said it was normal for her to not want as many bottles as long as she is still having a good amount of wet diapers but recommended I give her an ounce of Pedialyte a day so she doesn’t get dehydrated. I’m worried about her temperature going up just an hour after giving her tylenol. Does all of this sound normal for it to just be teething? Or should I set her up an appointment or even take her to the ER? I hate seeing her feel so bad. I’m a first time mom so I really don’t know what’s normal or what I should be worried about. She doesn’t seem like her gums are bothering her to me. She hasn’t seemed like she is in pain and she hasn’t been trying to chew on anything. I don’t know, any advice/thoughts would be appreciated though.

****Update in case other mamas go through this!!! my baby had a UTI they gave her an antibiotic to take for 10 days and her fever was gone the next day after taking it once.