Are the following sentences examples of comma-splice?
I am well, thank you.
I have been sick, but I feel better now, thank you.
If just one is a comma-splice example, why is one acceptable, and the other not?
A comma splice is using a comma to join two independent clauses. In these examples, "thank you" isn't an independent clause. Rather, in these examples it's being used as an interjection (sometimes listed in dictionaries as an exclamation).
When an interjection appears in a sentence, you usually set it off with commas. You can make it more emphatic by moving it into its own sentence, but it's not required, nor is it a comma splice if you fail to do so.