i have never heard that sighing can invalidate prayers. i do know that laughing out loud in prayer not only invalidates the prayer but also the wudoo.
stop worrying about what you think you may have done. just don't do it and if you do, then repeat the prayer, etc. Remember that Allah is most merciful and He knows about our weaknesses. He knows that we can't be perfect. we must only try our best not to do something wrong on purpose, for example laughing in prayer or breaking fast , etc.
wiswas are related to fear and worry. shaytan takes the benefit of a person's fears and makes matters worse to tire him out so that he will fail in worship and give up. so if you get thoughts like you may have done something but don't remember whether you have done it or not, then don't worry about it and just say that Allah is most merciful and will forgive you. but if you are absolutely sure that you have done something, then make up for it.