I feel like this is a stylistic choice. Commenters seem to be getting hung up on the OPs sentence and the use of the word "anyway," vs. the actual question at hand. If we replace that example with dozens of others, the question posed remains, and I believe is still valid.
"I smiled at myself, and walked over to her mini fridge to grab a water."
Clause one. I smiled at myself. This is an independent clause for sure.
Clause two. (I) walked over to her mini fridge to grab a water. With the implied subject "I," this is also an independent clause. In speech, a slight pause would happen between "myself" and "and." If the subject was repeated after the and, there would be two inarguably independent clauses and the comma would be required, but the sentence would sound clunky.
"I smiled at myself, and I walked over to her mini fridge to grab a water."
You can get away without the comma, but if you're reading this to someone or reciting it out loud, I believe a pause would happen there naturally, and therefore be indicative of a comma.