Upvote:3
Apply for your new visa, and attach commentary on your circumstances (along with a copy of any supporting documentation). I would think that since you're voluntarily disclosing the information, you should have no problem.
This assumes that there is no information available that matches your name and correct birthdate, that would have precluded you from getting a visa previously. Chances are, if your birthdate was just a few days or months out (as opposed to many years), they would already have figured that out, if it were the case.