Tomatoes can cause a variety of topical or skin reactions. This includes uncomfortable irritation of the skin due to acids in tomatoes. Skin contact with tomatoes can cause itching. In some cases, it can cause hives at the contact site.
These skin reactions are not immune-based. They are not the same as allergic reactions that happen after eating tomatoes. They are better classified as contact or irritant reactions. Immune-based reaction include symptoms in the mouth, throat, stomach, and respiratory system (e.g. cough, wheezing, and shortness of breath).
You can have a contact or irritant reaction after touching tomatoes, but not a food allergy to tomatoes if you eat them. If that is the case, be careful when touching tomatoes, but you don’t need to avoid eating them.