I need to prove Prove that the language L = {w | number of 11s in w is more than the number of 010s} is context free
Sketch of an answer:

As you suggested, use the states of the PDA to check when a $11$ or a $010$ has been found. Then, instead of keeping track of the number of $11$s and $010$s separately, keep track of the difference in their numbers.

You could have some symbol in the stack initially, say, $\$$, to mark that the stack is empty. Then, use a symbol $x$ to denote $+1$ in the difference, and $y$ to denote $-1$ in the difference.

Whenever a $11$ is encountered, and the top of the stack is not a $y$, push an $x$. Else, pop a $y$. 

When a $010$ is encountered, if the top of the stack is not an $x$, push a $y$. Else, pop an $x$.

Thus, at any given point, the stack consists entirely of $x$s or entirely of $y$s, or only the $\$$. The number of $x$s denotes how many more $11$s have been encountered as compared to the number of $010$s, and vice-versa.

At the end of the input, accept if the top symbol is an $x$, as this would mean that the number of $11$s were more than the number of $010$s.