My healing piercing is itchy... Is this normal?

Yes, very normal! The first part of your new piercing that heals is the OUTSIDE.  Part of that process can include some drying of the edge of the piercing - similar to how a scab can be while healing.

Make sure to soothe the area with use of a hot water compress rather than trying to scratch or pick at it. This will add moisture back into the area in a gentle manner and should resolve the itchiness safely and quickly.

Some resources may suggest the use of saline or other products during healing. I am not a fan of these for two reasons...

First, salines only really serve a benefit when warmed and the piercing is submerged as a soak. Sprays are largely going to evaporate from the skin surface, but may dislodge some of the notable serous deposits, aka "crusties".

Second, these products can be quite costly. Hot water compresses do not cost anything to perform. Nothing to purchase. Just a clean washcloth and water as hot as you can stand to wring with your hands. Simple.