Ah, yes sneezing is almost always a sign of illness. Once could be that he got some dust up his nose, but more than that usually indicates a problem.
I'm afraid its not safe to burn incense, have scented candles, use air freshener, spray deodorant, smoke or other similar things around a rabbit. Don't feel bad though, you werent to know, I did some of these myself many times before I knew, and I think it may have contributed to triggering Barney's snuffles.
Some background info on snuffles: Most rabbits carry the main bacteria that causes snuffles, and it lies dormant until the rabbit's immune system is stressed or weakened and then it sort of gets 'triggered' and becomes active. Sometimes a course of antibiotics sorts it out, and the immune system gains control over it again. But sometimes it doesnt, and there are usually periods where the bunny seems a bit better, or even completely better, but then it flares up and bunny gets symptoms, you fight it with antibiotics and other meds and it calms down again, only to start the cycle again. It is a frustrating illness to deal with, as it is actually incurable, you can never completely get rid of the bacteria, but that doesnt mean that your rabbit will always be ill, or that he will not have a good life. A lot of people panic when their rabbit gets snuffles, (I myself found it difficult to come to terms with the fact that there is no cure), if it is snuffles then try not to panic, a snufflebun can still live a happy and long life, and many people find that it flares up infrequently.
I remember you have insurance, that is good, I hope you are out of the 14 day exclusion period?
Yes, they should offer antibiotics - probably baytril as its the only one actually licensed for rabbits. You may also be offered bisolvon - which thins the mucus and makes more of it, which helps flush the bacteria out and helps to stop them getting bunged up. I love this medicine, I find it really helps.
They may also ask if you want a test done (culture and sensitivity test) on the bacteria in his nose - they'll stick a big cotton bud up his nose and send it away to grow the bacteria. By knowing the exact bacteria, it is easier to choose an antibiotic that works best against that bacteria, you see. But sometimes nothing grows and we are none the wiser and a little poorer! It isnt essential, and more use if the infection is ongoing, but bear in mind once they are on antibiotics, they have to come off for a time before they can have the test. Most vets dont offer it the first time the infection presents itself.
I would also get the vet to look in his mouth, especially at the back teeth, with an otoscope. Dental problems and snuffles are often linked, as are running eyes and dental problems. The pain from dental issues can cause the runny eyes, and so can the tooth roots overgrowing and pressing on the tear ducts, which is what the xray you mentioned would be to check for.
Of course , it may just be irritation from the incense, so keep an eye on it, and actually touch the wet areas, as when they dry they can still look wet. If they dry, it could just have been eyes running, no infection.