Yes, your confession was valid because the priest who heard it gave you absolution. It’s his job in the confessional to
judge whether you have made a good confession, and he only gives absolution if he decides you have. He has judged on behalf of the Church - and that is the end of it.
Of course, the priest can’t necessarily determine whether we have been truthful, or whether we have deliberately withheld a mortal sin, but so long as we have been truthful (to the best of our ability), and not deliberately withheld a mortal sin, then we are absolved.
Similar questions appear here from time to time, and some will argue that you are still obliged to confess any mortal sins which were omitted when the priest cut you short. Others, including myself, will advise you to accept the priest’s decision in this confession, and not revisit any aspect of it.
One thing we always agree on, however, is that the confession is valid, and even if there is an obligation to confess any omitted mortal sin the obligation is only to confess them at your next confession, without urgency. For the moment, you are absolved and free to receive communion.
On the subject of whether you need to “reconfess” the omitted sins, I recommend that you just ask a priest next time you are in the confessional. Not because I think you have to, but simply for your own peace of mind, ie. to eliminate any doubt or fear.
