If you are already in the US in another nonimmigrant status, you may be allowed to apply for a change of status to J-1. You must be maintaining valid nonimmigrant status in order to apply for a change of status.
Prospective exchange visitors already in the US will go through the same J-1 sponsorship application process with CGH. Once this process is complete, CGH will issue a form DS-2019. You will then need to pay the SEVIS I-901 fee and then file form I-539, Application to Extend/Change Nonimmigrant Status, with the US Citizenship and Immigration Services (USCIS). Form I-539 and instructions can be found on the USCIS website. It is your responsibility to complete and submit form I-539 and also pay any associated filing fees. You will not be able to submit Form I-539 until you have a DS-2019 issued by MUSC and you have paid the SEVIS I-901 fee.
It is important to note that you will not be able to begin the J-1 program at MUSC until you receive an official approval notice (Form I-797) from USCIS, indicating that USCIS has approved the I-539 application and granted you a change of status to J-1. Processing times for I-539 applications vary and are always subject to change, but in general these applications typically take around 3 months to be processed by USCIS. You can refer to the estimated USCIS processing times for more information. There is currently no way to expedite or premium process the I-539 application.
Because of the processing time involved with an I-539 change of status petition, it may be more beneficial in some circumstances for you to return to your home country and apply for a J-1 visa to enter the US, rather than applying for a change of status while remaining in the US.