There are a lot of things that could be at fault here, and it’s hard to say what it is in your case.
First of all, there is certainly some truth to the fact that females get preferential treatment in hiring. But there really aren’t all that many women you have to compete with, so you should be able to get by anyways. Besides, it also sounds like you are hoping that you will get preferential treatment because you have family in certain companies - this strikes me as a bit of a double standard.
If you’ve gotten that many interviews, your resume is probably good. Not necessarily perfect, but it gets you the interview. As for why you don’t get the job, it could be a number of reasons. Maybe you haven’t applied to enough jobs (you need to apply to more than you think because job searches are tough), maybe you need skills you don’t have (learn them to make yourself more marketable), maybe you just got unlucky enough to be outdone by some other candidate who was a better fit 11 times in a row (it happens), and maybe you are doing something wrong. Don’t expect HR to be honest with you either because first and foremost they have to shield themselves from lawsuits from unhappy applicants.
If you still can’t find an internship at the end of it all, I recommend you do the following: look at the specific skillsets that companies commonly want (CAD, programming, etc are big ones for MechE, for example) and learn them. Also learn to tell the employer exactly what they’re looking to hear in regards to your work experience, even if it is only partially true. Also helpful is to find a mechanical job, even if it isn’t engineering, because a lot of companies like that sort of thing. Is it better than an internship at a well-known company? No. But it is far, far better than doing nothing.
As for the GPA, I recommend putting 3.8 as your GPA if yours is higher than that. Trial and error taught me that that was the ideal GPA for appealing to most employers.