I got toilet water on hand after using the plunger. my hand has cuts from eczema. should i be concerned? there were no gloves around?

Water and soap will suffice in this context. The risk for superficial infections remains otherwise and you should try to cover at least the open wounds so that they do not get irritated during the day/work.

If you washed your hands with soap and water after the exposure to toilet water, there is little risk of any infection. Wish you good health!