Can untreated ADHD cause low emotional intelligence?

Okay, so stick with me here, ha.

I'm 28 and was diagnosed with ADD, Ring of Fire subtype, as a teenager. I've always been angry and depressed, unable to focus on anything that isn't fast paced (which is why I LOVE video games), sensitive to light/sound/touch/etc. I ended up getting an emergency appointment with a visiting psychiatrist because I was refusing to go to school and I was in a very dangerous headspace. He diagnosed me ADD and.... Then I never saw him again. The diagnosis wasn't even put on paper (if it was, it's long destroyed), so now I've been diagnosed with BPD instead.

Fast forward 14 years and I'm in a really crappy way with my entire life. I never finished school because I struggled too much (dropped out 15), I can't focus on ANYTHING, if I get bored I get incredibly depressed and I'm so sensitive to my environment that I'm prone to outbursts if it's too noisy or too bright. Because I've been given a diagnosis that doesn't quite fit now, the treatment I'm getting isn't helping at all. No matter how much therapy or how many antidepressants I take, I'm constantly the same way. Nothing helps whatsoever and I fear I've learned some really bad coping mechanisms that I can't undo. I'm starting to rely on dangerous amounts of caffeine, alcohol and benzos just to function.

Emotionally I'm super stunted as well, I haven't "grown up" and I still feel, act and react exactly as teenager me did. I'm prone to outbursts when things become to overwhelming, I'm easily agitated, I'm almost always depressed when I'm bored... I'm just generally unpleasant sometimes, and I feel like I can't control these things. I try, but the more I fight it, the worse it gets. I've been told I'm "too immature" and "too sensitive" a lot, even by my own mother.

Is this a common ADHD thing? I just feel so alone with it, I'm really distressed that I can't be the adult I need to be. I'm honestly trying but it's so hard and no one will help me because I'm "BPD" and being "difficult". I'm seeing both a therapist and a psychiatrist, but neither one believe me about the previous ADD diagnosis and seem to think I'm doing it just to get on drugs.