You Do Need power plug adapter while traveling from Barbados to Swaziland.

Here is Why You Need An Adapter

The outlet and plug type used in Swaziland is M and in Barbados are A and B. This is how they look like.

Barbados

In Barbados, outlets of type A and B are in use.

Type A

Type B

Swaziland

In Swaziland, outlets of type M are in use.

Type M