She may be doing this for attention- she may be scared that you are going to die soon, and therefore, so will she, and is looking for reassurance that this is not going to happen really soon, but in a very childish way. She probably knows that it gets your attention just by the look on your face or your body language, whatever the reason she has for doing it. Perhaps she has expressed fear to her mother (perhaps about when you are sick) and she has reassured her that she isn't as "sick" as you (because her lungs are fine), and this has been embarrassingly translated into these outbursts, and her mother is too stunned/embarrassed to know what to do. Just my thoughts, of course <img src=""> .
She should know better, and probably does; I am presently going through the stage with my 3 year old that "we don't point out (in a loud voice) that that man (who works at Walmart) only has hair on the sides of his head, you can tell mommy about it, but very quietly- it hurts some people's feelings", and once I point that out, she is sheepish and embarrassed, no matter how sweetly I tell her.
Perhaps if you sit down right after one of these outbursts and talk to her about it, they will cease. Tell her that it hurts your feelings, that she isn't "as sick" as you, and that since she is younger, she will probably have better medicines than you did anyways, just to do everything her mom and doctor tell her, if that is her fear <img src=""> . And it might not hurt for her mom to hear you say this, so she has an opening to step in and talk to her if she gets rude about it again. She may be waiting for you to say something, and take the lead, if you haven't talked about it . <img src="">
On the other hand, if she is just doing this for attention, she may need a stern talking to, and I would talk to her mother about this if it continues. It would then almost be like a toddler yelling a cuss word in the middle of a crowded resturant- it gets everybody's attention focused on her immediately, and if she did learn that info from her mother, she also has embarrassed her parent, who in turn does nothing. That is also a power trip. That may require disipline from her parents, not just an explanation and heart to heart from you. If she continues to be this way, you may just have to tell her that you won't be coming around if she is going to treat you that way, and when she is ready to apologize and treat you the way you treat her, to give you a call. Even my 3 year old understands that I am not going to play with her if she is going to be ugly. Good luck.