It may be sign of eye infection, or you may suffer inflammation. You need to do some remedies immediately. Use some artificial tears three times a day. See a doctor if you still feel burning the other day.
By the way, relax more can help you get rid of the discomfort. You can also drink some chrysanthemum tea to reduce the inflammation. Do not eat anything can promote your internal thermal such as beef and pepper.
People with burning eyes usually suffer a feeling of burning and irritation of the eyes, Also, it may accompanied with itching, tearing even discharge. And there are many reasons that can cause burning eyes. And I need you give me more information to know why you got burn in eyes when you lay down. Generally speaking, burning eyes can result from environmental pollutants such as tobacco smoke, smog, or dust or household items etc. Besides, Allergies, Conjunctiviti can also contribute to burn eyes. So, you'd better take an eye check first by eye doctor.
It looks like you are really worried about your eye health. As a matter of fact, it would be very strange for anyone of us to have such experience so there must be something wrong with your eyes. Generally speaking, that would be resulted from some infections such as pink eyes, trachoma, conjunctivitis, etc. So, it would be wise for you to have a medical checkup and take some following actions against your problem.