It seems like you are having some symptoms suggestive of inflammation around the surface of the eye. This could be due to dry eye, blepharitis or allergic conjunctivitis, to name a few possibilities. It would be best to seek the opinion of an ophthalmologist who would be able to conduct a thorough exam of your eyes and direct the right treatment for your symptoms.
With regards to blepharitis, it is true that warm compresses can be helpful. However, often times chronic cases may require medication in the form of topical antibiotic and steroids. Best to seek the opinion of an ophthalmologist to know what treatment is required in your case.
