I'm certain that's a Hickory (Carya sp.).
I agree that you should show the WHOLE plant first, then progressively detailed images. Always show how the leaves are attached to the stem/branch, which will always help separate similar species.
Hickory will have alternate arrangement of pinnate compound leaves; Ash will have opposite arrangement of pinnate compound leaves.
I have no advice for burning eyes - other than it means lots of tree pollen aggravating me here in the Ohio River valley...