I find no need to be completely smooth, so shave in the direction the hair goes. Or, I will use my electric razor, which doesn't cut close enough to make it itch. That's my preferable option.
Did you use sensitive shaving gel and moisturise it after? Do that and then the next time you shower (the next day hopefully) put in some baby powder, after that you’re all good
I suggest shaving in the shower and using a shaving cream on it before hand. Trim first. One tip is to shave in the direction the hairs are going. So if your hairs are growing downward shave down ward, this is to reduce ingrown hairs, and red skin.