There are some kinds of nutritional supplements for eye health. But it will take years to get a satisfying result. You can try beta-carotene. You just need to take a 5,000 IU supplement of beta-carotene daily. But if you are a heavy smoker, I will not suggest you to take this kind of supplements because it is linked with a higher rate of lung cancer in smokers. Besides, your skins may turn yellowish because it can accumulate under your skin bit by bit. So you must take an appropriate dose.
Vitamin C is good for your eyes. You can take in vitamin C by eating more fruits or take some vitamin pills. But I won't suggest you to take chewable Vitamin C tablets because they can dissolve tooth enamel. If you are suffering from glaucoma, you may need to take more vitamins (usually 2,000 mg to 35,000 mg daily). But if you have a history of kidney stones, you should take less than 60 mg per day.
Our eyes need all kinds of nutrients and vitamins. lutein and zeaxanthin, vitamin C, zink, selenium, copper, turmeric and manganese are all good for our eye health. But you have to pay attention to the amount of these nutrients. Sometimes, take in too much of them will lead to side effects. Besides, I have to remind you that you can't take them if you are under any medical treatment because they may have chemical reactions. Hope this helped!
I am sorry that I can't give you specific eye supplement for corneal erosion/ inflamation and melanosis. Once my eye surgeon told me that there is no proof these supplements work. But I suggest you to eat plenty of different colored vegetables and mixed peppers because they are good for your eye health and they can prevent retina problems.
I think you may need to see an eye doctor immediately. Maybe some medical treatment is better than eye supplements. Corneal erosions and melanosis cannot be helped with supplements. Maybe there is a kind of ointment which can help solve your problems.