Well first of all you should understand that fairness creams can make you look only a shade or two fairer but cannot help your natural skintone. Second of all, you are beautiful however you are and you don’t need to be fair to be so.
Now, let’s get down to business. Can you sue them for misleading you in their advertisement? Let us look at how effective that lawsuit will be? There are three bases on which a lawsuit can be filed: Breach of contract, breach of trust and tort (Tort is a civil wrong that does not amount to breach of contract or trust. Causes like negligence, defamation, malicious prosecution fall within tort. ) And then you find a lawyer who is willing to spend their time and resources for this cause. Now tell me, even if paid tremendously, which lawyer would want to engage in a legal battle against multimillion dollar companies who would brush this away. Hence, even if possible, this would not be a wise move as the benefits out of filing this suit will be negligible.
It would make for a proper legal battle if the product caused some kind of tangible harm in terms of your dermatological health. But otherwise, even though it is possible, it is not worth it.