Compatibility summary
You will need a travel adapter in Antigua and Barbuda; plug types used there differ from South Africa.
Plug comparison
South Africa plug types: C D M N
Antigua and Barbuda plug types: A B
There is no common plug type between South Africa (C D M N) and Antigua and Barbuda (A B). You need a travel adapter.
Voltage comparison
South Africa: 230V, 50Hz
Antigua and Barbuda: 230V, 60Hz
Voltage difference is within a range many devices tolerate; check your appliance label.