A full yes from me, Lyme can cause food allergies.
I had a severe imbalance of my gut flora and leaky gut prior to treatment, causing food allergies and intolerances.
about the fruit: another possibility is that you might have a fructose intolerance. I have this. Headaches are typical for fructose intolerants.
Like Razzle, I would advice an allergy test, and an appointment with an experienced nutricionist. Someone with enough experience is able to determine what you might be intolerant for, things that haven't shown up in the allergy test, just by questionning you and listening to your complaints.
I am in no way affiliated with this lab, but the following is a very good lab for food allergy testing: USBio Tek Laboratories. It's the lab my dr uses, and I'm in Europe.