For example, a couple of years ago I talked to this woman who had lupus, and she would often tell stories of the all the gnarly surgeries and medications she had to take to control her disease. I rather got the impression at the time she enjoyed the attention it brought her; not necessarily in a totally overbearing way, but more subtle.
Similarly, just today at the barber's, I overheard another woman talking to a hairdresser about some disease she had, which required her to take "experimental vaccines" and "all sorts of red and blue pills"; she informed the guy that although she looked outwardly normal, she was felt terrible, and was sick all the time from the medication. She gave an "I'm chugging through it" half-smile as she talked.
Note that this isn't Munchausen's, which is the first word to come many people's minds — neither of them ever gave me the impression they weren't truly sick. It's more they had an enthusiasm for being ill and sharing that news that most people don't have. Is there a good word for this kind of person?