Venting about my past relationship and how I've struggled

I met her online and things were great! We moved in together and were able to show her things she would have never dreamed of. We went skydiving, to Disney, and drove a super fast car for her birthday. We celebrated our first anniversary and minus some disagreements, I was happy.

She has a lot of animals and I was helping her with caring for them since she would receive weekly infusions for a medical condition. I'm a breast cancer survivor myself so I had limitations. I accidentally gave her cat an early dose of her medication and it led to having to euthanize her. The cat was 19 years old and had hypothyroidism, high blood pressure, and arthritis. Although the vet and I said it wasn't my mistake that caused her to pass, I do blame myself.

Once this happened, she asked me to stay with my family until she grieves. My fear of abandonment got the best of me and I would try to fix what happened by reaching out or calling her. She pushed me away more and more. I spoke to her best friend for guidance, but I got upset and took my belongings and turned the keys in to her mom. I know I might have pushed too far and I regret my behavior. She knows I would never hurt her or her animals. I check in from time to time because while she told me to give her space, she felt like I didn't care about her emotions.

I would like some insight into what steps I need to take to move or continue to show that I care because I genuinely do. She saw me for who I am and this mistake and my behavior created a wall between us. Please no judgment.