I think the same happened to me with LEDs. I have an odd feeling that I can't really see a small section somewhere close to the center of focus, not directly at it. I remember an odd sensation in the eye for days after dealing with a white LED.
Here's how to spot it:
Hold you hands together, with thumbs up, at arms length. Close your left eye, and slowly move your right thumb away to the right, while looking at your left thumb. At around 6 inches it will dissapear.
It's kind of hard to notice when my thumb is static, but it's more obvious if I wiggle my thumb while doing it.
They can, however, do an extended version of the blind spot experiment above for the whole field of vision, where they project light dots into a hemisphere in an unpredictable but iteratively somewhat exhaustive fashion. Very tiring and challenging test, since you need to keep your eyes from wandering, fixated at a boring reference point for more than half an hour. Like a hearing test, but for your eyes...
Laser beams or high energy radiation in general may also damage vision elsewhere in the optical pathway. Like opacification in the cornea or vitreous body when proteins get denatured by the heat. The body is very bad a repairing any damage in the optical apparatus since the eyes do have their own blood barrier, so macrophages usually don't have access to clean up "junk", and most tissues involved aren't really regenerative. Worse, damaged proteins tend to slowly spread the faulty structure to their neighbors.
Don't fuck with your eyes!
Your brain can fill in a lot of voids before you notice, especially for monotonous areas and static impressions (as mentioned the blindspot or the blood vessels on your retina are usually "invisible" until you provoke awareness through unusual lighting changes, or defined peripheral accounting experiments). You likely won't notice acquired "blindspots" looking at a white wall, or chaotic fallen leaves on the ground, especially where the other eye provides missing information, but at the edges of highly predictable patterns, one eye closed at a time, you may trick your brain to fuck up, eg. blur or indent otherwise clearly defined areas, when it can't decide which color to fill. Reading texts with on eye closed may also highlight "dancing" letters or distortions around your center of vision.
Worth noting, such defects may be caused by progressive conditions like retina detachment or even ocular melanoma, and the association with laser/light accidents may be incidental. If you spot a spot, do not brush it off as a limited loss! Have it checked, even with a likely attributable cause. You may prevent full blindness through medical intervention in case of disease!
Edit: You can see the blood vessels when you look a white wall and steadily move a (smartphone) flashlight in and out of the field of vision, slowly waving the light next to your head, illuminating from your ears to the side of your nose and consequentially your eyes at a shallow angle. This will cause an unusual blood vessel shadow, now meandering through your vision. The blood vessels are also very visible during eye examinations when the doctor moves the slit lamp around (go check it out ;)
Very weird seeing the insides of the very eye seeing, by ... well ... seeing.
Edit: Never mind; misread.
If you had say UV LEDs, all bets are off since it wouldn’t trigger the pupillary light reflex to close down the iris.
Make a grid in a drawing program with crosshairs in the centre. Close one eye. Keep looking at the crosshairs. Scan from the central focus point using your mouse and click when you can't see the mouse cursor. With a bit of trial and error you should be able to map out large regions you can't actually see in.
(My dad did this years ago for a retinal detachment spot in his one eye.)
More importantly: get an optometrist to check out your retina.