jmc

If the two containers that held 11 eggs each held 12 eggs, then the number of eggs that you have would have been a multiple of 12. However, two eggs were removed, so the number of eggs you can have is two less than a multiple of 12. Therefore, the number of eggs you could have can be written in the form $12c-2$, where $c$ represents the number of containers you have. As a result, we would like to solve the inequality $12c-2>100$, which has solution $c>8\frac{1}{2}$. Therefore, since the number of containers must be an integer, we must have $c=9$, so the smallest number of eggs you could have right now is $12(9)-2=\boxed{106}$.