Can I get into HBS or GSB

How did you get a job as an analyst at a top group of you went to a mediocre school and had a mediocre gpa? Family connection hook you up? Or just luck?

Candidly it will be very challenging based on what you've shared.  With that said, if you can get a senior MD at your firm to really go to bat for you or if you can find some other way to differentiate yourself, you never know. Theoretically, a knockout essay could put you over the top, but I'm personally skeptical how much that really moves the needle (I'm sure others will tell you differently).

A bit hesitant to bring this up since it's out of your control, but it would obviously be more likely if you were a female or an under-represented minority. I say that only to give you a more realistic sense of your chances.  

But all of that aside, why do you even want to go to HBS/GSB? If you want to stay in the HF world, you're better off just sticking around or trying to lateral. If you want to pivot into something like consulting/tech, don't fixate on HBS/GSB, you could accomplish the same thing going to any Top 10 b-school (and likely get a scholarship while you're at it). If you want to do something like PE/VC, candidly you're facing a pretty uphill battle even if you do go through HBS/GSB, so that's probably not a great reason either.

Leaving aside the question of why you would want to do an MBA, I slightly disagree with the general trend and think you have a very strong application (at least for HBS, which likely cares about GPAs less than Stanford due to the size of the class). 

Adcoms put you in buckets, hence why a few mentioned the finance/banking one is very competitive. However, they typically look at patterns to see where you have overachieved (for example, a Harvard grad who is working in a Big4 job after college would be in a worse position, application wise, than a non-target, first gen student who came from a poor family background an ended up at a Big4, even though on paper one has Harvard on their CV). So, in your case, even if you don't like sharing personal stories, that is the best thing you can do for your application, as it clearly mitigates your GPA. And what proves you are both smart and an overachiever is that you still somehow managed to get a top BB out of your situation, and then a top hedge fund. 

Therefore, based on your story, as a person who grew up in a single mother household, is a first gen college grad, and lost their parent during college and had to take care on their younger brother, still got into a top BB in NY, you have achieved what many would not be able to from your position. 

So 2 things in my opinion are still important and could tank your application: 1. Not getting a strong GMAT (740+, ideally 750+), which I assume won't be an issue given your job progression; 2. Not being able to articulate clearly why you need an MBA - people in your position would likely stay in their current role or switch funds, if they are outperforming.  

And congrats again on overcoming your setbacks earlier in life.