I hate to be the bearer of bad news here....
First of all let me start by saying, no, in my opinion, he should not be doing this to you. That aside...
1. You DO have to qualify for FMLA. You have to have been employed with them for 12 months and have worked at least 1250 hours during that time.
2. If you do not qualify at the time of the birth of your child, YES, the time can and in most cases will be counted in your absenteeism limit. Most companies use a revolving 12 month cycle when they look at absenteeism.
3. Sick time is a BENEFIT that does not have to be offered by any company. You are lucky that they let you use it when it was your child that was sick not you. If you use more than they give you, is is considered excessive. And it looks like you did since you dipped into your vacation time. I don't know you didn't say for sure.
4. The office manager is not your boss. She can say what she wants to you but it means nothing unless it came from him to begin with.
All that aside, as an HR Director, I would never treat an employee this way. Especially if these were the only instances she had of missing work since she came to work for me. You never said just how many days you missed due to the flu and ear infections. If you are a valued employee, he will just let it go. If you feel uncomfortable working there, like this is hanging over your head, I would start looking for another job. I am sorry you are being treated this way, but it is not illegal.