You'll be fine.
Firstly, Psychological studies have proven that when presenting to an audience, presenters who made mistakes and errors were liked MORE as people than presenters who made no mistakes. Its because you're seen as human, people relate to it, and flaws can be endearing. Google it if you dont believe me but its true!
Secondly, we all have wobbly moments. It doesnt mean you'll be wobbly tomorrow at all. All it means is, you had a bit of a moment today- no big deal. Tomorrow is a fresh start and a clean slate.
Thirdly, If you were in the audience watching, what would you have felt? would you have thought, "wow- what a stupid horrid pathetic bitch that presenter is"? OR, would you have thought- "oh that poor woman, she's clearly having an emotional moment, I hope she's ok- thats the kind of thing I would do!!". I bet its the second option. What would you tell your best friend if she had this problem?
Finally, take heart. Oprah Winfrey was an evening news reporter and apparently got fired because she couldn’t sever her emotions from her stories. Eventually she was fired from the producer of Baltimore’s WJZ-TV. Now she's the richest woman on TV! People LOVE her emotions.
Tomorrow, focus on your breathing. Make sure you breathe out longer than you breathe in. Deep breath. You'll be amazing tomorrow.