Amazon has a ton of foldable hats with UV protection in all colors. Most are fairly inexpensive. I bought this one for a beach trip and it worked out well (although somewhat pricey):
Coolibar UPF 50 Women's Beach Hat - Sun Protective (One Size- B... https://www.amazon.com/dp/B01F2F5CS2/ref=cm_sw_r_sms_awdb_t1_gS1BAbGSM5GD1
Wide brimmed packable hat with UPF sun protection fabric and a string to fasten it under the chin in case of wind. Any regular fabric has a super low SPF, so ideally you want something with UPF if you’re sensitive to UV. Plus a wide brimmed hat helps protect the face too.
Random example: https://www.amazon.com/Coolibar-UPF-Womens-Beach-Hat/dp/B01F2F5CS2