Hi there, I understand. It's tough being a mom and not feeling like a "good mom". But you really are a good mom.
It seems like you would benefit from some private therapy. I have been seeing a therapist for a month now and she helped me see my issues for what they are. She helps me see that it's NOT my fault, I am not a bad person, and I do have good intentions despite what I show to everyone else.
If you can stand the feel of them, invest in some ear plugs. I bought some and had to use them in my last apartment. I couldn't handle anyone's noises through the walls. Noises for me goes both ways. I can't handle multiple noises going at the same time, but I also can't sleep at night in utter silence. I need a buzz sound, so I bought a fan I run all night.
Have you thought about explaining to your kids what's going on with you? I find that explaining to my kids that mommy has a hard time with ____ or ___, they seem to really try and listen and care and want to help me not struggle. My boys learned that if mommy isn't functioning, nothing will get done that they want to get done. I don't mean to do it in some "feel sorry and worry about me" way, just say listen, I have a hard time with it when you all repeat your words or talk at one time. It's good to show your kids you are human and we all struggle. I told my kids I have SPD. They are so curious to know what it is, and my 10 yr old googled it and asked a lot of questions.
Anyway, hang in there cause as you can see you are NOT alone.
Don't let guilt bring you down. If you can, try meditating daily for 5 minutes at a time. I do Yoga 2 times a week and meditate for 5 minutes daily. I cant do more than 5 minutes at a time, but it's better than nothing. It helps calm me down.
Be well