No you cannot..

Last year I changed job after applying h1-b petition. My case was selected in lottery and I received 797C. For some reason I had to move and change a job and my H1 petition was cancelled. I talked to my lawyer at that time and he said the transfer can be done only after October. Thats when my status actually changes from F1 to H1 so that I can transfer my employer on H1.

Yes you can. If your H1B is approved, you don't have to wait until October to transfer it. I don't know what happens if its not approved yet.