He keeps stating that Im uncaring of him and our relationship

Its been a little past a year since my boyfriend and I dated. Its been going great and now we're completely comfortable with each other, we tell each other everything that bothers us towards each other. We've been talking more and be more open. He tells me that it seems to him that I dont care much because I dont reply to him quickly or that I dont care cause Im always busy whether its being with my family, work, or talking to my friends. He feels that Im ignoring him because im talking to other people and not calling him because I have to sleep or have to be with my family (my family doesnt like it when Im on the phone, consider rude). He got upset with me one time because I wasnt showing enough affection through texting and assume I didnt care, also when I 'ignored' him for while that he deleted me on facebook. He was really upset and tells me that he really cares for me which I believe. Would I be consider an uncaring girlfriend if I dont always consider his feelings even when I cant control on what I can and cant do? How do I prove to him that care and love him and that he doesnt need to worry?