dry eyes can be a very annoyinig problem. From what u described, i believe you have dry eyes. The firstline basic treatment is topical lubricants, but there are other measures that can help ease, if not totally cure, your dry eyes condition. Clinical assessment is necessary to see which type of dry eyes u are suffering from , and from then on targeted treatments. Lately IPL is a new treatment modality to dry eyes. Other things like punctal occlusion is also possible.
Your dry eye condition may be related to the radiotherapy treatment of the cancer. If that is the case, very likely you need to use external replacement of your tears by frequently application of the artificail tears. Try to use every 2-hourly, suggest to use non-preservative eye drops. Some other methods amy help, but need to assess your eye condition before prescribing.
Depending on how deep the pigmentation is, can use diathermy or surgery to remove the pigmentation. But best to assess first to see how big and how deep the lesion is.