I am surprised means I am now surprised. "Get" stands for an alteration. That is to say: " I become surprised." If you want to emphasize your change in attitude , you ought to use "get". Provided that you intend to highlight your continuos surprise, "am" is supposed to be used.

1) I was surprised. It's the past tense of the verb "be". When I think of the verb "Get" (rather Got in this question) it's something you can possess or 'have' as opposed to how you felt in that moment. So for the example above it would still be "I was surprised by a squirrel jumping out the tree."

They're both correct but I think your second example would often be followed by more detail. Example: I got surprised by a squirrel jumping out of the tree.