Seeing a busy woman

Just to get you up to speed ive been talking with a girl i used to go to school with, shes a good hardworking woman, and she doesn’t have an addiction to her phone or social media similar to how I am. She lives 4 hours away and is currently in school and working full time. Recently shes been having family problems and health related problems. She really is busy and when we find the time to sit down and talk she definitely shows interest and has no problem telling me deep personal things about herself. However she often falls asleep or gets busy with school and doesn’t text back for a few hours. I don’t have a reason to think she’s seeing someone else but I just want advice on how to deal with the silence in between the time we get to share together. I understand love is patience but I just cant help thinking maybe im exhausting her or annoying her. Im trying to be a loving and caring partner to her but it feels like she wants time for herself everyday and I just don’t know if im pushing her away. Hearing from her everyday really makes my day better and shes genuinely engaged when talking to her but I just don’t want to push her away. How do I deal with the silence?