If you feel as though your locks need moisture, it is completely appropriate to use a light amount of hair oil (if you are comfortable using oils in your hair) or conditioner to help hydrate and soften them. If you feel the itchiness is due to dryness, conditioning them may help. You don’t need anything fancy; a storebought, inexpensive, major brand conditioner will work just fine.
The only thing you need to be careful of when conditioning/hydrating your locks is that you fully rinse the product from your hair. It’s the same with shampoo. Don’t slather your hair in the product, and be sure to rinse 5-10 minutes after you wash.
Now, sometimes locks are just itchy. This might be more true for straighter hair as it “wants” to stick straight out more than wavier and curlier hair textures. I am not 100% sure of this, but it might be the case. My former partner was always itched by my locks when we cuddled, but they never really itched me.
It may simply be that your locks itch you- you may get used to it and you may not. It may also be the point of maturity they’re at right now. Maybe in two more months they will feel less itchy because they’ve tightened a bit.
You can always wear a light scarf over your neck or wear your hair up during the day to keep it off your skin.
I hope this helps you!