Hey everyone I really need some advice on my current binding issue.

Now I've bought such a variety of binders and such from Underworks (it's the only company I can buy since theyre on amazon and buying amazon gift cards is discreet) and the only binders that seem to get the job done and give me a flat chest are the  "Extreme Gynecomastia" ones that are tank tops (The t shirt is like super crew neck and you cant hide it at all) So I get the tank tops and they work fine and I'm all smiles UNTIL I see huge bulges of underarm fat sticking out and creating lumps in the backs of my shirts and whenever I pull up the tank to hide the fat it just comes down again once I start moving my arms. Does anyone know how to fix this? It's so embarrassing and I just want to be happy in my body and I think if I can fix the armpit fat problem I'll be alright.

I can tell you my experience here. You may not like all the conclusions I personally have drawn, but they're all I've got.
I've been on hormones for a year and still have to bind. No matter how well I can hide it, I am still constantly paranoid about my chest. Even though I am stealth and only one person knows where I work, I am always paranoid because I can tell. But the reality of it is no one else can. i don't know your exact situation, but most of the time we are making it worse than it really is in our heads. That's just my mental tidbit of thought. As for actually getting rid of fat bulges, my suggestion would be to exercise and lose weight. I'm in the process of doing this myself. The chest tends to fade first, so this is really a good plan, in my opinion. Doing a lot of chest exercises will help decrease size.
I apologize if this is a bit scattered, I'm quite tired. I do hope I've helped in some way.

Unfortunately that is the trouble with binding when you've got a bigger chest. What I did to mask it was layer.

Wear the binder flat against your skin. Push your chest either up and out or down and out. Put a tanktop over this. Try to find one that has tight armholes. Pull it up so that the front is as close to your neck as possible. Tuck it in, then put another layer on top. This should help a bit.

It's not ideal in the summer, but it's the best I've found.

I wear a tight v-neck tshirt under my tank binder.
Then I get creative with arranging the front circles (boobs) to achieve maximum flatness with the least amount of fat bulging out the arm holes. I usually push them down and to the sides a little.
As for the tank falling down, maybe consider stitching the arm straps do they're a little shorter. Not sure I understand the situation though.