I've been having itching going on beneath my eyes and looked it up. I found that cold air outside and low humidity in the house can cause dry, irritated skin. Well, that has been the way of it lately a lot where I live- cold air outside, low humidity inside.
I read that cold compresses, patting dry, not rubbing, and using moisturizing cream were things to try. I read the skin under the eye is thin and delicate and the advice not scratch. I think allergies were also mentioned and they might have suggested looking into things if you had started anything new lately, such as new make-up, etc.. I was concerned for awhile my eyedrops might have been contributing to the problem.
But you have an additonal problem of itchiness inside the mouth- did a bit of research and found a response about an itchy mouth lesion by a medical professional on medhelp:
I was wondering, with your having taken antibiotic if it set you up for a yeast type of infection, as antibiotic kills the good bacteria along with bad. You might consider taking acidophilus capsules and see if it does anything positive for the itchiness in your mouth.
Also, the cough with phlegm and the nausea feeling- it might even be that you have acid reflux and if you did have some allergy or allergies you are unaware of, that would increase phlegm production and could make acid reflux even worse. Acid reflux can potentially cause a cough and nausea, so you may want to have an ear, nose and throat specialist look at your throat for signs of acid reflux.
Please see an allergist and get tested to find out if you have any allergy/allergies you are unaware of so you might become armed with knowing what you need to avoid or might want to start getting treated specifically for your particular one(s) if it turns out you've got any/them. I think the pollen is supposed to be particularly bad in the southern state I live in this season.