Apple has published info on materials and allergies: Wearing your Apple Watch - Apple Support
Apple Watch Ultra (GPS + Cellular) (Titanium): titanium case, sapphire crystal, ceramic back
Apple Watch Ultra 4 (GPS + Cellular) (Titanium) and Apple Watch Ultra 4 (GPS + Cellular) (Hermès): Sapphire crystal, Retina display, and ceramic back
Selected bands are listed, can vary, and some bands can potentially contain nickel.
Other issues can involve skin conditions including dermatitis, or allergies to other trace materials.
Check too with your allergist or other appropriate medical providers.