I know that this response is long, I tried to hit all of the points just so that I don't post a bunch of responses. You do not need to feel like you must answer all of my responses, or any.
First I want to say that being a "guy" doesn't mean you can't have feelings, be sad or frustrated, vent or anything else. It doesn't hurt your image as a man to express your feelings and let people know you are a human being.
I have a few questions/clarifications about your personality and anxiety that might help us and you make sense of the situation.When you talk about affect and emotion when talking about personal things, are you saying you lack it? Or feel you use too much of it?
I do not feel that being quiet is unhealthy... I am a very quiet and reserved person unless I am comfortable with someone. I had a few friends, but if I didn't have a class with them I never talked to my peers unless forced to. In college I am sure my teachers thought I was strange because I never talked to anyone unless they talked to me first. Do not think it is bad to be quiet or reserved. In regards to getting consumed in an activity, my brother in law is that way, as is my husband. They both can get so drawn into what they are doing that a crying baby isn't enough to bring them out of their zone. This is normal behavior (and is often seen most in males)
This may seem strange, but Chase Ross just uploaded a video about "toxic masculinity" and he talks about how there is a type of masculinity, described in the extreme of the generalizations (including no emotions, misogyny and the like) and how they are dangerous for all men, but trans men in particular. It is so easy to get caught up in the male stereotype and attempting to fit that that we often forget that as men we can be feminine and soft as well. That it is okay to embrace that femininity for the sake of our mental health. (this includes being quiet, emotional, chatty, or anything else).
We are all people and are all unique in the ways that we express ourselves, we shouldn't feel like we have to fit a mold that most cis-men do not fit themselves.
I agree that it can be frustrating to live your life as a quiet, shy, and anxious person, I too struggle with this. Don't push yourself too far too fast. Maybe go out where no one knows you and challenge yourself to ask a stranger a question (safest to ask about the location of something so it isn't intruding) and go from there. But I cannot stress enough that you have no need to be outgoing if you do not feel that way. Especially if you have already done so for the sake of work. I can tell you from personal experience that if I spent all day smiling, talking loud enough for people across the room to hear, and holding up non-sense conversations.... I wanted NOTHING to do with talking or touching for a couple of hours after. Now that I only engage with children I can still do those things after work.
I hope that you manage to get enough blood draws for your internship, if I lived close I would suck up my anxiety and fear of needles in order to help you. The thing with interning.... If they are not teaching you than they are not doing right by the program. The ONLY reason interning works is because we can prove that unpaid interns learn more than they benefit the company. If they are not teaching you than you are not learning more than you are helping them. An intern should be being taught.... I know it can be tough, but maybe find someone who you get along with and ask them for advice on how to get more experience and draws? I will admit I know little about how the field works as needles, blood, and the squishy parts of people freak me out.
You say that your personality is horrible, but you have a girlfriend, so you must be doing something right.

But, again we come back to the toxic part of masculinity for you, the need to be "the man" and all of the extremes it comes with. (I totally get it in terms of her wanting to be a submissive, which might be easier once some of your dysphoria is dealt with) but it is totally okay to let someone else make choices and choose activities, just make sure you speak up if you do not like them. And if you cannot speak up to your S.O. than maybe that person isn't right for you as that person should be the safest space you can go to to talk.
Honestly, I can only tell you that if you want to be dominant, be loud, be hyper-masculine, than you will have to push yourself out of your comfort zone to do it... and maybe you will find it suits you... but maybe you will find it makes you more miserable.
It may be awkward and annoying to you, but unless others tell you they find it that way too, do not assume people do not find it cute. (my hubby sure does) HOWEVER, even if they do find it annoying, it doesn't mean they don't care for you and aren't willing to work with your anxiety and individuality.
I am confused as to what 'credibility' you are concerned about.... Your credibility as a man? As a person? 'Street cred' is often something used to express how hyper-masculine a person is, to show off how strong, superior, etc they are... honestly, not something I personally admire in people... I have found that I am more confident when passing as a man, I can talk to and ask questions of store employees in ways I cannot in my fem clothing. I am laughing more, more outspoken with friends and family and generally happier which makes me want to engage with the world around me.
I do still fear that I might say the wrong thing, but remembering that I can always try again helps.