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Your experience doesn't confirm the validity of the new rite.  Emotions and feelings are not sacraments.  Also, your experience does not mean that every new rite priest is actually a priest.  All your experience proves is that Christ gave you peace through some exorcism prayers.  

Why would Our Lord Jesus Christ allow a man outside the Church to speak with His authority?  Exorcisms are efficacious when and because the minister has the authority of Christ.  Does Christ give His authority to those who belong to non-Catholic religions?

Demonic Obsession

Back in the early 1980s, I received some help from Father John Hampsch of the Claretians, but it was only temporary.

I had stayed at the home of one of my business associates while she was visiting Europe, but unbeknownst to me, that "friend" had a set of tarot cards, so I began having demonic nightmares. Even though those Tarot cards were revealed to me in a mystical way, and I was able to find and destroy them, the demonic nightmares continued. I sought the prayers of Father Hampsch, and they were effective for a few months, but they returned. While this was not demonic possession, but rather demonic obsession, it was still very scary.

Finally, months later, in desperation, I sought the help of a traditional priest, and I was able to sleep without fear of being haunted in my dreams.

https://comeholyspiritconferences.org/bios/rev-john-h-hampsch-c-m-f/

Note: Father Hampsch was ordained before Vatican II in 1952, so his prayer life seems to be more devout, but he does celebrate the novus ordo mass and is part of the Charismatic Renewal, which has its own problems, namely that of ecuмenism, where he has prayed with Protestant ministers as part of Charismatic ministries.

The traditional priest used the prayers of exorcism from St. Basil and St. John Chrysostom. These two prayers are short, but extremely effective.

These two prayers can be used for oppression, possession, and curses placed on an individual.

They are in the Book of Needs used by Eastern Catholic priests. My priest was bi-ritual saying the Latin Traditional Mass and the Byzantine Divine Liturgy.