Might be worth just getting your eyes checked again - just to make sure you're not getting a recurrence of the ulcers. Unless you're putting your head in the chalk bag or really rubbing your eyes with chalky fingers climbing really shouldn't be a problem. Try Blink drops, it's what we mostly use at work for patients after laser surgery as well as for contact lens wearers with dry eye. Your work sounds like a more likely source of irritation, than the climbing.