general question amortized cost and worst case lets say a data structure has operations called insert and delete both of which take O(log(n)) worst case. Suppose the amortized cost of insert is O(log(n)) and the amortized cost of delete is O(1). 

Now if a sequence that has n delete operations performed on this data structure  that has n elements currently, then what is the worst case? If delete takes O(1) amortized cost does this mean the worst case (not amortized) is O(n) for n delete's ? 



I think no because it doesn't seem right but I'm not sure how to explain it
The answer hinges on the definition of amortized cost. Since you haven't given such a definition, let me assume that you are using the common definition.

Consider a data structure supporting operations $O_1,\ldots,O_m$. These operations have amortized cost $T_i$ (where $T_i$ could depend on parameters) if the total cost of a sequence of operations run immediately after initializing the data structure consisting of $c_i$ many operations of type $O_i$ is at most
$$ c_1 O_1 + \cdots + c_m O_m. $$
This bound only works if we consider all operations done on the data structure since initialization.

In your case, you are only considering one part of the operations performed on the data structure, and so amortized cost doesn't apply.