Do you fail often at work?
I ask only because it seems like you don't; eventually something you should realize and let the stress fade away and replace it with confidence you will kick ass.
I don't. The problem is that when I don't necessarily hit a project out of the park my competency gets put into question. I could hit 99 home runs but that 1 "outfield ground ball" is what stands out.

Also, the constant need to get a bunch of work done before 5pm is crazy as well. Right now I'm in the middle of making a presentation to persuade my higher ups that we should be breaking things down (like a website design) into smaller "stages" over multiple days instead of trying to nail the whole thing in one day. Sure it'll take longer but it should improve the end product by leaps & bounds.
What a lot of people don't realize about "creative" jobs is that you need some time away from a project to give your mind a break. Especially if it's a complex project. That way you can come back to the project with fresh eyes and see solutions to problems that were not apparent before. Also, there's a process called "steeping" where you work on something really hard and then you step back and let your subconscious wrestle with it while you go for a walk or do some other mundane task.
The only problem with "steeping" and my job is that I'm usually "steeping" during my off hours because that's the only time I have to do it. Thus making me restless and unable to sleep.
One summer in college I worked at a newspaper distribution warehouse (graveyard shift) and would easily sleep 10-12 hours during the day. Completely unproductive outside of making some money. I blamed it on my body not dealing with graveyard shift well.
After college, I worked in a production lab where everything was following an SOP and meeting deadlines with long stretches of boredom in between. My sleep schedule again went to shit.
Right now, I work on the PM side of a utility dealing with regulators, stubborn union vets, and upper management that never worked in this department. I feel a lot more stress than ever but I sleep soundly because when you have work goals that aren't just based on monotonous, repetitive work, it's a lot easier to feel motivated.
I think your problem is that you hate the type of work you do. You obviously are able to work hard, but maybe there's nothing your current workplace asks of you that makes you feel satisfied?
Some of my work is monotonous. Some of it is challenging.
I think the real problem is that I'm not doing what I really want to be doing. Making cool shit for myself and the people who resonate with my "vision".
Instead I'm trying to make other people's "visions" a reality since they themselves couldn't design their way out of a paper bag.
I'm a visual artist trapped in the corporate design world since graphic design was the only career path that I hated the least compared to everything else I could've been.
Anyways, now that I have some of my energy back, I'm going to try and make my artistic vision a reality during the weekend and possibly early in the morning on the weekdays.