Is it dust as in crumbled bits of hay or a fine spray of dust every time you pull hay?
If it is a fine mist, please THROW IT AWAY!! If the farmer is saying the hay was baled damp then it is very likely your hay is mouldy. If this is the case, prolonged exposure to the spores (dust) is the cause of farmers lung.
Regardless of the weather, damp and fusty hay should never be sold! We had awful weather here too, but we still have dry hay. It isn't nutritionally as good as the hay crop last year as it was cut and baled later, and there is only just enough to last but it ain't mouldy.
A silver grey patch in the bale, dark brown or black places or a smell similar to tobacco are all signs of dangerous hay.
Please be careful!