If you suspect something is wrong then it probably is. But if she's given you no reason to believe that she's after your money then maybe you're just imagining things!
This might sound outrageous, but you could always say that your family are going through a tough time financially and that you'll have to budget more, and see how she reacts? I'm not sure that lying in a relationship is the solution, but it's not a lie that will hurt anyone and if she genuinely likes you for you then she'll understand. She'll obviously deny it if you approach her directly and I can't imagine that would help your relationship in any way.