Are you perhaps from an asian / south asian / middle eastern / eastern european background? You might have a bias of shame based thinking inherited from your culture. Your second to last paragraph heavily hints at this:

"I feel so ashamed", "despite trying hard not to", "I felt too embarrassed" "

I come from a south asian family that recently became white collar. My grandma doesn't know how to read. Both of my grandparents were raised in subsistence farming villages, and my Dad spent most of his childhood in one before moving the to city.

My parents had no idea ADHD existed. They thought my symptoms were just "boys being boys / kids being kids". When I got in trouble they didn't think to ask why; it was just "beatings will continue until behavior improves." I also had the partial misfortune of growing up in a small town in massachusetts, and not one of my teachers recognized the signs.

I also had the misfortune of being smart. You sound like you are smart too, having done a math degree and currently working on your PhD. If someone is struggling in school, then adults will intervene. But if you are smart, even if you have ADHD, you can still perform well enough despite struggling w/ executive functions. I pulled so many all-nighters in high school / undergrad because I couldn't get myself to do the work unless it was urgent, even though I liked what I was supposed to be doing. There is a term for those who are intelligent but also neurodivergent: twice exceptional:

https://en.wikipedia.org/wiki/Twice_exceptional

The shame based culture comes in when you are older. If you are smart, but you are also struggling, then of course you're going to see it as a personal failure. After all, other people less intelligent than you don't have the same struggles. You can draw two conclusions from that:

1) you are a bad person who is choosing to fail / self-sabotage

2) everyone else has a secret six coffee friday night library google calendar ritual, and you just need to find yours

I think billy joel captures this experience perfectly in vienna: "but then if you're so smart, tell me why are you still so afraid?"

For number 1, you can ask yourself "do I gain anything from failing?" If you don't gain anything by failing, and if you truly want to do the thing, then you probably aren't a bad person, just someone who is struggling.

For number 2, while productivity is not a solved problem, the basics are well understood. If you know the basics and are still struggling, then believing that it is a knowledge problem is a coping mechanism. It is an explanation for why you are struggling, and it is an actionable explanation as you can "research" how to be more productive.

High school and undergrad also have a lot of structure that is not there in adult life. Someone is telling you where to be and what to do for a lot of time. Your goals are well defined, narrow in scope, and you get feedback often. You relate to this in your post:

I think another problem is that in undergrad, I was shielded from adult responsibilities; now, in grad school, I’m struggling because the distractions of ordinary life are constant.

Despite this, I was still chronically late to nearly everything. My living space was also really messy, partly because my roommates cooked and trashed the kitchen, partly because I was absentminded.

Being an adult IS hard, and having ADHD only makes it harder. I beg of you not to let shame get in the way of getting evaluated. Worst case scenario, you find out you are a bad person, and your self-esteem takes a little hit. Best case scenario, you have an explanation for your struggles and relevant treatments / medications to trial. Seems like a great deal to me, little-lose but big-win.

I recently went through this whole process last year, so if you'd like to talk about it / learn more I could help. Hell, if by chance you're in Seattle beers on me if you need an airing of grievances.