First, teaching is incredibly stressful, inner city schools especially. Is this something you are willing to deal with in order to teach? There is a reason these great offers are made for certain areas. That being said, these areas need good teachers too. Also, do you think your illness hinder you? Once you know the answers to those questions you will know if this is something for you.

Secondly, I wouldn't disclose your illness if possible. If they ask why you were out of work, tell them that you were experiencing medical problems that have since been correct/dealt with, etc. You don't need to go into further details. As long as you can pass the background check there shouldn't be a problem with you working with children (assuming you aren't a danger to yourself or others).

Do not lie. You can be terminated immediately for lying. As far as I know, they cannot terminate you due to mental illness. However, if they really want you gone, they will find a way.

If this is something you want to do, I think you should try it. If you don't try, you'll never know. You sound like you will be very effective.