If you check websites (e.g. Latuda Side Effects in Detail - Drugs.com for "Latuda side effects," you'll find itchiness listed as infrequent.
You're apparently one of those especially sensitive to something in this med. personally, I'd tell my pdoc and find something else. The goal do treatment isn't to trade miseries.
I have a bit of skin sensitivity from Topamax, like pins pricking now and then, but it's occasional & the benefits are enormous. It's up to you, but I'd want to know there wasn't something better for me.
Welcome to PsychCentral. Keep coming back, & let us know what you decide.
Roadie