Is it normal after being exposed to sunlight for awhile to have small dark spots appear on your skin they look like freckels?

It can be normal. Well, sun exposure certainly causes your pigment to darken. However, certain medicines can have a sun-induced hyperpigmentation. Most likely though this is simple sun-induced pigmentation. From what you describe this may be what's called solar lentigo. Of course having a dermatologist examine it will help you confirm the answer.