Good advice. Thanks to all! We have two more meetings and I will resign at the next one with my official resignation beginning on the last day of school.

The way I understand it is you don't want to be the President anymore? Correct? If that is the case, then leave. Submit your resignation and move on. The term limits would apply to the next person to step in like jonwilson said. So starting now. Your group will hopefully and likely find a replacement for you soon enough and although there might be a brief scramble, they'll find their bearings soon enough.
Give the resignation with a time limit though. Don't just walk into a meeting and quit, give them some notice but be strong. They made an agreement with you that they would find a replacement so that had to know it would come.
Mum24 said it right. You are not a servant. Follow your instincts.

I think if you want to stay and the organization wants you to stay, it shouldn't be an issue.
Normally, a change takes effect as of the date it is approved. Meaning from this date forward, the term limits apply to you starting with this year.

if there were no bylaws when you were elected you have no set term so you leave when you want and no one can make you feel bad about what you have given of yourself in your time served!! Two year terms have to have an out clause anyway what happens when peoples circumstances change after just one year and they are no longer able to serve they have to be able to walk away without everyone giving them a hard time!! Life changes daily for everyone just let them know and be polite but firm in your resignation!! Good Luck!

They were not in the bylaws before the elections. In fact, I wasn't supposed to stay on this year, It was an agreement they would find someone to replace me this year and I would assist until a replacement was found. They looked for other positions, but not for mine.

I don't understand how a change in the bylaws after an election covered by the old bylaws can include you?? They cannot backtrack unless that was listed in the bylaw change, was it?