If you are using the pool and testing at the right time, you will always see CC. When the FC reacts with anything in the water, CC will be formed, then eventually broken down the rest of the way and disappear again. That is maybe oversimplified, but it is how I understand it. Someone please correct me if I am wrong. So CC is not necessarily a sign of a problem, but rather a sign of the chlorine doing its work.
Now having said that, 1.5CC seems pretty high. So it may be a sign of a need to SLAM. But I would second Dom's suggestion of doing an OCLT to decide if a SLAM is needed.
The low CYA does seem a likely culprit. However, even with CYA down at 20, shock level FC is 10. So unless your CYA is WAY down there, it may be something else. And if your CYA was 50 in May, it would seem like something unusual had to happen to drive it that low. Even if you drained or backflushed or vacuumed to waste or overflowed your pool enough to remove and replace a THIRD of your water (5000 gallons) TWICE it would still only get you from 50 to about 20. That is unless something happened like an algae bloom that consumed the CYA.
The other thing I would be thinking about is pee. If anyone is peeing in the pool, it will eat your FC like crazy and produce significant CC pretty quickly. And the chloramines that are formed hang around a while and cause burning eyes and the stereotypical "chlorine pool smell." If that is what is going on, feed it enough chlorine to keep the FC up, and give the pool plenty of sunlight which helps break down the chloramines.
But I would still follow the recommendation of Dom and others. Get your CYA up to a reasonable level. If that was the whole problem, that should fix it. If it does not, do an OCLT to see if you have something in the water that needs a SLAM. And if the CYA is good, the OCLT is good, and you are still having the burning issue, then I am thinking pee is the issue.