Does my baby have a slight fever?

Brittany • wife to henry, mama to norah + chloe

My daughter is 12 weeks old as of tomorrow. She had her first round of vaccines on 01/08/2018. She had TDaP, Hep B, Pneumococcal Conjugate, and Rotavirus. It’s now 01/12/2018 and she felt warm to me to I took her temperature rectally. She’s coughing every once in awhile, and has a stuffy nose, and overall crabby. Her temp was 99.3F. Is that a slight fever? I know they said to take her to the hospital if it reaches 100.4 but I was just curious if this could be why she’s acting the way she is? I’m a first time mom so I’m trying to learn as I go. She’s also drooling a lot so I was wondering if she could be cutting teeth? I starting cutting at 3 months old.