In this case, can I say "I got it" instead? What is the difference between "you got it" and "I got it"?
Answer from a Native speaker
"You got it" is an idiom that is used to express agreement to do something for someone and implies that you will get it done quickly. "You got it" is similar to saying "yes" or "sure", although it is used when someone is specifically asking you to do something. It is only ever said as "you got it" and never "I got it", because "you got it" means that the person you are doing something for will get the result of what you are doing. If you say "I got it", this has a different meaning, and just states that you understand but not that you agree to something. Ex: A: Can we get two milkshakes? B: You got it! Ex: A: Can you make me some dinner? B: You got it!