Many people get mild lip or tongue tingling or itching with fruit, where this is due to allergy it is sometimes called oral allergy syndrome, particularly when you get symptoms to lots of different fruit. It is due to birch pollen allergy (ie hayfever), very similar proteins are found in fruit (particularly those with pips inside and a peel eg apple, pear, peach, plum, cherry).
You may find that you can eat the fruit if peeled, tinned, cooked or processed (eg jam). The ripeness, even the specific species, can matter too. Some affected individuals even put up with the itching because they prefer not to miss out on their favourite fruit!
However, a significant proportion of people with oral allergy syndrome can end up having a reaction that affects not just their mouth, but skin, lungs etc in which case there is a chance of having a more serious reaction or even anaphylaxis.