Justin,
How did you set up the scratch disk(s)?
You can change their location in the settings of PS, and also specify a directory in which the swap file is going to be created.
This will enable you to check for yourself the size of the swap file being created by PS, and to understand better why it is telling you that it is full.
My guess is that the default points to the C: drive which is often a smaller partition aimed mostly at containing Windows and some apps.
The basic recommendation is to use a separate disk as a dedicated scratch.
Cheers,
Bernard