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i doubt you fractured your sternum just because there is cartilage connecting your ribs to your sternum and its more likely that this costal cartilage is just inflamed from all of that energy being dispersed from the back into itself. But i would see a doctor just to be sure.
i had the exact same thing in december/january of this season.. i landed on my back and then my buddy was like "hey is your chest okay" (he knew my chest is gonna hurt because he had it too some time ago and he told me he could HEAR it when i fell.... but dont ask me how haha) then i asked him why the hell he asks me about the chest when i clearly landed on my back.. but he was right and it hurt really bad everytime i fell or moved my upper body too hard for 2-3 weeks. it really wasnt nice at all but it should be okay (nothing broken or anything)
and yeah sneezing was a fucking nightmare!