NO, you cannot. You must travel outside the US and apply at an embassy or consulate for the F-1 visa with the newly approved change of status approval but this is always risky. One use to be able to apply for a visa at the Visa Office of the US State Department (in the US in Washington DC) but they closed this option for non A and G (diplomats and UN Visa holders) several years ago.
Congratulations ... you now have status as a student and should keep in close contact and frequent communication with your foreign student adviser.
He/she will explain that you need a 'real visa' if you leave the US. If you don't leave the US, you don't need a visa.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.