Don’t be so hard on yourself. You didn’t sabotage your relationship. In fact, you didn’t do anything wrong. It’s entirely possible that your medical crisis had nothing to do with your girlfriend starting to date someone else. You’d only dated for about three months in total, and it’s entirely normal — and even probable — that the relationship wouldn’t work out because one or the other of you didn’t find the other compatible. It’s just numbers, or the luck of the draw. That’s why dating IS a numbers game. The more people you date, the more likely you are to find Ms. Right, as long as you’re dating smart.
It sounds like your crisis and your girlfriend’s attentiveness and kindness made you feel like there was more there than there really was. In fact, if you hadn’t had had your crisis, she may have broken up with you sooner, but because you did have problems, she decided to stick by you. But now you’re well, thank goodness! 🙂 Your girlfriend was a real stand up girlfriend in your time of need — but it would be wrong of her to lie to you and pretend that she had feelings for you that aren’t there.
She wants to be civil at least and friendly with you at most. It’s entirely fair for you to continue to try and pursue her, but if she keeps saying no to your attempts to date her, then it would be wise to back off.