It is possible for someone to have wood allergies.
There are some types of wood you could develop an allergic reaction to, sometimes only after a long while wearing them.
The allergic reactions can vary from itching to irritation to swelling or even necrosis or anafylactic shock. The latter can become fatal.
So pay good attention when buying your jewellery. Always.
Woods people can develop allergic reaction to are: Rosewood, Tulipwood, Sonowood (another type of Rosewood), African Blackwood, Teakwood, Willow, Macassar Ebony, Birch, Sugar Maple, Camphor Wood, Red Oak, some types of Bloodwood and there are more…
Woods you want to avoid for these reasons are: Afromosia, Australian Blackwood, GreenHeart, Mansonia, Sassafras, Satinwood, Cedar, Redwood, Pine and Yew.