You do sound insecure. She gave you feedback so let's look at it.
1. If you're gonna do something that causes her to alter her routine or life in a significant way, then that's worth having a talk about. If you just want to do something nice, don't fucking ask to do it, just DO it. This includes things like making breakfast, cleaning up after yourself, or running errands for her. I.E if she says oh man I'm so busy today I have A B C D E to do then you can follow up with "oh wow you are super busy today. Don't worry, I've got dinner covered tonight. Text me about a half hour before you get home so I know when to have it ready." It shows that you care about her, and are taking charge. You sound supportive without being a doormat. If she says no thank you in some form or another, then you simply back off and say "ok np! If you need help with anything lemme know <3 "