Some deodorants irritate me as well.
I eventually found out that it was a "72 hour" deodorant that I was reapplying every 24 hours (after my shower where, I assure you, I was washing my pits) and it was building up. It was so itchy and I'd scratch until I was raw.
Now I only wear it every other day and use a "natural" deodorant in between.
Might be different for you, obvs
Clearly the winning choice 😁