I would take the money and go to a regular therapist. Talk about why it suddenly started bothering you, work through insecurities (old and new), and get yourself in a better place mentally. Being able to speak fluently won’t mean much if you are still unhappy with and worried about your speech. Like others have mentioned, practice speech techniques on your own, but if I were you I’d talk to someone, especially since you mentioned it never bothered you before. Chin up you’ve got this!