Hi, Binger.
Your dragon is almost certainly suffering from mild photo-kerato-conjunctivitis. It is like "snow blindness" - what people get if they look at very bright sunlight on snow, or arc welding light, without proper sunglasses - the UV damages the very delicate transparent cells on the front of the eye, the "cornea".
These cells are killed and have to regrow. It is really painful. People say it is like having glass or sand in your eyes. Your dragon keeps his eyes closed because of the sharp pain, it certainly will make him miserable and grumpy too. (Some dragons are so upset by the pain they totally collapse, and this is very frightening for both dragon and owner)
Fortunately, as soon as he closes his eyes, the damaging UV is blocked and the eye starts to heal. The moisture behind the closed eye helps, too. Healing is very fast and as it heals, the pain stops.
Many dragons open their eyes in about 2-3 days, some can take up to a week. If there was worse damage, though, such as "sunburn" of the eyelids too, these can swell up and healing may take a few days longer.
If you are worried, do take him to your reptile vet, but unless there are definite signs of an infection (oozing, weeping, bleeding or sticky discharge) there is not any need to use antibiotics, ointments etc..
It is best not to try to
bathe the eyes with water or home remedies, or make him open them, or even to force feed him if he won't eat. As soon as the pain stops, he will feel like eating again. If he hasn't eaten or drunk for several days, though, it's probably a very good idea to offer a drink of slightly warm water to keep him
hydrated.
When this condition first appeared with some compact lamps in 2006, I wrote a web page about it here:
http://www.uvguide.co.uk/phototherapyphosphor-info.htm
Do keep him at the right basking temperature, this is really important. Buy a household incandescent lamp of the same wattage as your
UVB bulb- a flood reflector is best - and put it in the fixture that had the
UVB bulb. Measure the temperature you get under the lamp, and adjust the height and/or wattage till your basking zone is back to 100-105F.
The white light from an incandescent bulb contains no UVB and will not harm his eyes or slow down the healing - but being cold will slow down everything and could make him ill.
I hope this helps, and that he is soon recovered.
Best wishes,
Frances