If you have done your best to confess all your mortal sins and did not purposely omit any mortal sin, your confession was valid and you need not repeat it. If a mortal sin remained to be confessed but you were not allowed the opportunity to confess it, your confession was still valid. Just mention the mortal sin next time you go to confession.
While the priests probably should not have cut you off, please understand that when priests start hearing a litany of venial sins, they likely assume that you have finished confessing all of your mortal sins. As venial sins do not require confession, a priest may become anxious to wrap up your confession so that he may hear as many confessions as possible in the time allowed for confession. The priest may also be concerned that a litany of venial sins is a sign of scrupulosity that he does not wish to encourage.
One way to handle this is to make sure to mention any mortal sins first. Once that is done, confess any venial sins you would like to confess. If you get cut off again then you need not worry that you have not mentioned any sins that must be confessed.
Confession Validity by Jimmy Akin