Hello everyone! Can you tell me what to do?

Hello everyone! Can you tell me what to do? I'm completely lost. My baby is six months old, and yesterday evening her temperature was 38.6. I panicked and gave her Nurofen, within 30 minutes the temperature dropped to 36.9 and she fell asleep. I only then read that with such a high temperature, you shouldn't give any fever reducer. This morning she had her temperature up again at 38.6. What should I do? There are no symptoms of a cold, no coughing or runny nose. She's a little sleepy, plays with toys and smiles, but she's just a bit fussy. Can you tell me what this could be? And