I've had mild eczema on my fingertips and knuckles on and off for years. It seems to break out when I am under stress. The skin gets rough and can crack - can be painful. When it does come out, I have not found hydrocortisone or anything over the counter to be helpful in the long run.
You have to get some prescription medicine. Currently I use Triamcinolone Acetonide cream, 0.1%. Over the years others have been prescribed for me, but this one works and is relatively inexpensive. It is actually covered by my insurance, but from what I understand even if it were not it is inexpensive compared to some other treatment creams.
As far as moisturizers, there is one called Aquaphor Original Ointment that the doctors gave to me that I believe is available over the counter as well. They recommended this in addition to the prescription cream.
Whenever I have a little outbreak, which isn't even that often, just one or two days of the Triamcinolone clears it all up.