As an adult, I've developed allergies to various fruit - peaches, apples, pears, cherries, nectarines and more.   organic too what could be the cause?

Oral allergy syndrom. These symptoms are usually due to a reaction to proteins in fruits and vegetables that cross react with (are similar to) proteins in pollens. This syndrome typically only occurs upon eating the raw fruit and vegetable. If you can tolerate these fruits in cooked or processed forms (apple juice, apple pie, canned peaches, etc.) this confirms that oral allergy syndrome is the cause of your symptoms.
Tree pollen allergy. If you are having local itching, swelling, or tingling of the lips, tongue, or throat after eating fresh fruit, then your body is likely reacting to proteins in the fruit that are similar to birch tree pollen. If you don't have problems with cooked fruit and if you have hay fever symptoms in the spring, then this is the most likely explanation.
Protein sensitivity. Fruit allergies can cause itching, irritation and burning in the mouth after eating certain types of fruits. This generally occurs in people who allergy to pollen from trees. Most often these symptoms last a few minutes but if large amounts of the offending fruit or vegetable are consumed dangerous anaphylaxis can occur. This occurs in 1 - 2 % of patients.
Oral Allergy Syndrom. If your reactions are local- oral and throat itching and burning- the problem is oral allergy syndrome, which is a cross reaction with pollens. It causes local irritation, but isn't dangerous. Reactions like hives, lip/tongue swelling, and wheezing are consistent with true food allergy. A positive test doesn't mean clinical allergy, just sensitization.
Oral allergy. A very common seasonal allergy patients complain about is oral allergy with fresh fruits. Some of the proteins that patients react in trees, grasses, and weeds are very similiar to the proteins to fresh fruit. Knowing your seasonal allergies may help. Also seeing an allergist will help determine how serious these allergies are and whether a patient may need a epi pen as well.
Allergy. Dr. Vallury is correct. Also research on a reputable medical website about oral allergy syndrome. This should help.
Pollen food allergy. It happens a lot in patients with pollen allergy, up to 30% by some source. There are shared proteins between certain pollens from trees or weeds with certain fruits, such as peaches, apples, cherries, or melons, etc. Patients who have those pollen allergy can be allergic to those fruits.