Can my visa status be changed from F1 to H1 because of...

Currently I am on F1/OPT and it will expire on march. My son is born and he is now USA citizen. Can I change my current F1/OPT to H1 or some other category. I have done masters in information technology and currently I am not emplyeed anywhere. I am still searching for job.

Does the birth of my child in USA can benefit me in any way (regarding visa status)?

Having a child who obtained citizenship by birthplace does not give you any benefits on visa status. You must maintain your legal status like others. However, when your child reaches the age of 21 and meets the requirements to sponsor immigrant visas for the parents, then he/she can petition you.

Maintain you status, do not overstay your visa, or you won't be qualified to receive immigrant visa in the future. If you overstay the visa more than 1 year, you will be bar from entering US for 10 years.