In Virginia, you are suspended by DMV based on the facts you have provided. The DMV suspension for failure to pay fine + court costs will be removed after you pay the fine, courts costs and DMV reinstatement fee.
I don't understand why you ask about appealing your license suspension.
If you are suspended in VA and SC as a result of failing to pay small fines associated with speeding violations, I suggest you pay the amounts due to both states so that your ability to drive can be reinstated.
T. Kevin Wilson, Esq.
The Wilson Law Firm
9300 Grant Avenue, Suite 301
Manassas, Virginia 20110