The reason your beard is itchy is because when you shave, you are essentially creating little spears on the tips of each hair.
They finally get long enough to bend around and poke at your skin. Your neck is very suspect to this because of the angle where the neck meets the head.
1) “Man it up” and just wait. It’s only temporary and will pass shortly.
2) Apply ample amounts of moisturizer like a beard oil, or other product. Try to avoid moisturizures with alcohol in there as they actually dry out your skin.
3) In the early stubble phase (day 1 or 2) use Soft Goat scruff softener. This product is designed to help make stubble softer and more kissable.