Eye watering happens only for a few reasons. One, some irritant is in the eye (dust or small particles of substrate could easily be the cause), infection or inflamation of the eye, eye lid or tear duct can cause watering. External parasites could be lodged near or under the eye lids can also cause tearing. If the eye is swollen or bulging out constantly the problem could be an abscess behind the eye, the sinuses etc.
As many have already suggested, I would get rid of the bran (never felt that was a good substrate to begin with, as it clumps, molds, harbors bran mites, parasites and is way to shifty (ie hard to get traction or even stand on without sinking to their armpits, depending on the depth) but people have used it with no problems. But as it keeps getting stuck on the eye lid and forming a hard crust, swap it out completely and use paper towels. At least this prevents the substrate from making the problem worse.
Next, take your dragon to the vet, especially if the eye doesn't get better after a couple days off the bran. A vet can do blood work on your dragon to detect signs of infection. Even if no puss is oozing out of the eye, doesn't mean there isn't an infection. A high white blood cell count will. He can also flush the eye to make sure there isn't any particle lodged under the eye lid which isn't being washed out by the tearing. He can also check for external parasites (though engorged ticks or mites may be visible on a close examination with a magnifying glass yourself. However, if your dragon did have external parasites, there would be other signs, such as moving bugs on the dragon, or left in bath water after you give him a soak).
Having pets of any type, be they reptiles or cats and dogs, does require responsibilities, which include taking them to a qualified vet when they are not well. Just like if our children are sick, we take them to see a doctor, we are responsible to do that for our pets. We can give advice here on the forums, but the truth is, none of us are qualified reptile vets. And the few that may be, recommend taking your animal to see a vet as it is very difficult to diagnose a problem without actually examining the animal directly. We definitely can give advice on proper husbandry, food, etc. but when something is wrong that doesn't involve increasing basking temps, UVB exposure, feeding proper foods etc, there is very little we can recommend that would work, other than bringing your pet to a qualified vet.
Thus, using an ointment for an eye infection or recommending you do that, may not work at all. If the cause of the tearing isn't an infection, then the ointment isn't going to help. In fact, in some cases, it may just make things worse. So a proper diagnosis is very important.
It may seem I am really emphasizing in your case, but in truth, I am addressing all who have sick or unhealthy dragons to see a vet, whatever their money situation. There are ways to pay for doctor's bills. Most vets will treat the animal first, then get payment from you, be it in monthly installments or up front. Call the vet, ask if have monthly payment plans for big bills. Express that your animal is sick and you do want to get it properly cared for. Most will let you pay in monthly installments. Some may even charge you less knowing you are short on cash. The examination and treatment may also not be as much as you fear. A basic examination may only be $45, a fecal $20 and bloodwork, maybe $100. As the editor of Reptile Magazine put in his comments to a letter he recieved in the recent issue, 'Cost of pet $10, Cost of cage and accessories $40. Cost of Vet bills, $150. Knowing your pet was taking cared of and now healthy: Priceless.' I found this such a good point had to paraphrase it here.
-----
PHLdyPayne