Let the hair grow in a little and see if you can ascertain which direction it grows. Shaving in the same direction of the hair should cause less likelihood of irritation. The tricky part is most people have hair growing many different directions under their arm, and it makes it tough.
Are you having irritation after shaving? Or, do you have a permanent state of irritation, redness and bumps? If you live with redness all day under your arms, you likely have folliculitis. For that you can try to cure it yourself by not shaving for at least a week, and applying hydrogen peroxicide to the area twice a day for a week. When you do shave your razor needs to be very sharp. Some people, especially women, are never taught the importance of a sharp razor. When it is sharp it quickly cuts the hair, when it is dull it pulls on the hair, and irritates the skin, and allows bacteria into the hair follicles. If you typically use a razor for weeks, try throwing them away more often for a new one.
If your irritation is immediately after shaving, could be an allergy if you are using shaving cream.
I shave my entire leg. Directly behind my knee I naturally don’t have much hair though.