Yeah, you can change your F1/F2 stauts into H1B. If you have an employer and is willing to apply for you, then you are good to go. Once you have your H1B approved, you can even go apply for the Social Security ( I assume that being in F2 sometimes it is almost hard to get one). Make sure you are in valid status. Also, where did you get your degree, it is helpful if you have foreign degree, you might want to evaluate it before submitting a petition on your behalf against USCIS.