How do I deal with the guilt of living?

I lost my guinea pig Cookie yesterday. My family and I are taking it very hard. I have this immense feeling of guilt that I have to continue my life and fulfill my basic needs like eating when she was struggling to eat in her last few days and is no longer here. I feel guilty doing anything, especially anything fun to cheer myself up. This is my first time losing a pet. I don't know what to do, I'm just consumed by this feeling of guilt.