If you truly wanted to know how she felt, you would not get upset at her if she did not respond to ALL of your texts.
I believe you are texting her regarding her illness to have an excuse to text her in the first place. It is for you to get a thank you for caring text back from her. This is how it comes across to me, do you think it may come across to her like this?
Let her come to you, have her be the first one to text or call or speak, then you can her ask her how she is doing. Try this, unless you think your way is working.