Dealing with a sick infant 😩

My 8 month old son started daycare last week and now he got sick. It started on sat night when his his temp was at 100.2. We gave him some baby Tylenol and in the morning his temp went down. He also has runny nose/ really stuffy nose. It has been over 2 days and his temp keeps going up and down. We have been giving him Tylenol and also baby ibuprofen and that seems to help bring his temp down to normal range. But hours later, it would go back up to 99 range. First time mom and first time dealing with a sick infant so I’m wondering if this is normal that temp keeps going up and down? And how long should I expect this cold to last? When should I be concerned and take him to a doctor? He also threw up earlier after we gave him Tylenol. Also, do you suggest we continue to give him Tylenol and ibuprofen until he’s completely back to normal? We don’t like giving him too much medicine but it seems to help. Any advice on how to clean and get the sticky and hard snots from his nose is greatly appreciated as well. He does not like it when we get near his nose and the shots dry up which makes it even harder to wipe off. 😩😩😩😩. Last couple days/nights has been tough 😩😩