We can't diagnose you, or anyone else. That's between the professionals and you.
But... being transgender is largely self-diagnosed, and simply requires some sense of a gender incongruity between the body and mind. I would guess that this gender incongruity exists in you, from what you have written here, so my personal opinion would be that you could very well be a transgender person.
Being genderless, or agender, also can fall under the transgender umbrella. I and others here have mentioned feeling genderless when very low. In my opinion this is a symptom of the deep depression and anxiety we can feel when we are trying to deal with the discomfort we have felt for a long time from our gender incongruity.
Being busy is actually a way that some of us cope with this discomfort. It lets us think about and focus on something other than our gender issues, essentially a distraction from our issues. I often felt even more down when I dodged facing my issues and dove into work.
I don't think this is an ego trip or something not real for you, based on what you write.
Getting access to therapy in some form could be a very good first step for you, to help clarity your thinking and better express what you are going through and dealing with.
Be well, Katie, and find a path to joy from here.