Does anyone know how I can easily just switch the colors of this image

As already suggested, you need a larger size of the graphic to make anything close to an accurate reverse colour of it.  I had a go, but I have no idea if I have every detail right.

Hi @AJDogMom, there are several ways to go about it. It would be best if you have a larger file to work with, even if this ends up being the icon size.

Create a swatch of the blue color with the eyedropper tool. Create a new fill layer with white and place it under the logo layer. Select the logo layer. Use the magic wand tool while holding the shift key to select all the blue area. Hit the delete button to remove the blue and reveal the white background layer. Inverse the selection, make sure the blue swatch color active, and use the Paint Bucket tool to fill the white areas with blue. Took me less than a minute to do it that way, but you can further refine the selections with feathering and so on as needed. Hope that's helpful.