Is it normal to just be more alone while dealing with something?

Normally I'm a very social person but recently I've been hit with a health problem which is going to take some time to get over. It isn't anything serious but it isn't something I can just ignore. Because of it, I've become more reclusive and have stayed away from social events for the most part. Even going out for lunch. It's just that I like to deal with my problems by myself and I don't like talking constantly about something which bothers me. I've kind of told some people at my work, my friends and my family, but they just don't seem to get it. They get upset at me when I decline to go some place and take it personally. I've even noticed some people getting frustrated with me and it just makes me even more annoyed. I'm not expecting the world's smallest violin solo but I think it is ridiculous to get mad at me because I want to get through something by myself. Is there something else I should be doing so they don't take it personally?