It depends on whether a change of status or consulate notification was requested on your H1 petition. If there is an I-94 attached to the I-797 then you are likely already in H1 status. If there is no I-94 and it lists a consulate at the bottom, then you must obtain a stamp before starting in H1 status. There are several issues that may exist if you obtained a change of status and are unaware of this. You should consult with an immigration attorney to get guidance on this.
It depends on whether USCIS changed your status or not.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.