Binni,  you can consult with a immigration attorney since you need one as u said ur employer is not going to file your petition for u, as far as the payment concerns , you can tell them to pay and make it deduct on ur salary which should not be a big deal for u, note the point the fees should be paid by the h1b petitioner which is ur empolyer so hurry up an consult a immigration attorney n he will tell u wat the employers need to do n what u need. good luck