What's the best way to cover my egress window (not soft plastic) where the window is above the window well?
I would recommend against the flimsy dome covers bib recommends in his answer/comment based on safety concerns with children. However, he is on the right track with a domed window well cover, you just need to search for one designed specifically for an egress window that supports weight, covers the full well, and allows egress. Here is an example http://www.egresswindows.com/product/Dome-Cover-5600-Egress-Well/window-well-covers-grates (note this not an endorsement of the linked product).