She really won't get very far with this!
Even if she could prove that she really did actually 'slip' and that that slip was caused by the eggs (which had been well cleaned-up) then i'm sure BB's legal team will point her to page 568 of the Rule Book which states in miniscule writing that the waiver form she signed before entry leaves her unable to sue BB or any of the housemates.
If this wasn't the case then i'm positive that at least one of the money-hungry desperados who enter the BB house (especially in recent years) would have done it by now.