You can always upgrade the H-1b to premium processing using from I-907 and paying the fee if you seek a quicker response. In terms of qualifying for EB-2, more information is needed, specifically if you have a 3 or 4 year baccalaureate or other higher degrees before you obtained your experience. Generally EB-2's will require substantial academic degrees, it just depends. Also, unless you are seeking a National Interest Waiver (NIW), you cannot straight file and EB-2 immigrant petition.
Ricky Malik, Esq.