Or perhaps you feel so lonely that you seize upon any show of affection towards you, from someone you are attracted to, and convince yourself that it has to be because they could be falling in love with you.
I've experienced both of these. I don't think they're unusual attitudes. And they are by no means the only possible answers to your question.
A person showing you affection is not always due to romantic love but it is due to love of some kind. You thoroughly deserve any affection you are shown by your family, your friends or anyone else for that matter! You can be justifiably proud of yourself for this. Just take things a little easier, that's all. Try to enjoy the development of relationships with others without becoming anxious about making it into a romance.
Your Grandmother could have any number of things going on at the moment and her actions may not be due to mental illness, as such. But it is very difficult for children to accept that there may be something wrong with their parents, so your parents may have some resistance to the idea that their mother (or mother-in-law) has mental problems. It is right and proper that you care for her and look out for her but do not jump to the conclusion that no-one else in your family does. And you should certainly not take it upon yourself to feel solely responsible for her. It is awful to see someone you know change like that but you can't take that sort of thing on your own shoulders. It has to be shared. No-one can take that kind of weight alone.
Are you at school or college or what?