There are 'western' riding helmets. Head safety should be a concern. ESP when you are new. NEVER refuse a helmet.
I have been riding for years, I have broke, trained, given lessons, managed barns and I still always wear a helmet. Even on my old reliable 22 year old horse that I have had since I was 17 (we know each other as well as any horse/human possibly can).
I have had a friend die from riding a boring school horse type. Even the most calm horse can 'have a moment'. I also had a student who's life was saved with a helmet. Not from the fall, but the horse was startled and kicked out. Got her in the head (we are talking 17hh powerful warmblood) shattered her helmet, she was still knocked unconscious and needed stitches from some of the outside of the helmet being pushed through the padding. But she would have been dead with out it (this was also a super calm lovely horse who she had been riding since he was started)
I could go on with examples. But trust me, helmets are worth it, doubly so when you are new.