Was the person serious about baptizing you?
Yes
Was the water plain natural water?
Yes
Did this person baptize you in the name of the Father, and of the Son, and of the Holy Spirit?
Yes
If so it sounds like a valid baptism.
So far, so good yes, lol.
Immersion is OK. A tub is odd but OK. What the person doing the baptism thinks about Catholics is immaterial. If the person intended to do what Christians do when they baptize it was probably OK.
I agree, that is how it happened.
If it was Mormon or Jehovah's Witnesses those would not be valid, nor from the Oneness Pentecostals, nor for fruity baptisms in the name of the creator and sustainer and redeemer.
I agree. She was from a nondenominational Church, and judging by the doctrine it seems like it is of Baptist theology for the most part.
Was the person who baptized you a recognized ordained minister?
No
Did he record the baptism in an official record of some kind of church. Did they provide you with a baptismal certificate?
Unfortunately, no to both.
I ask these things because the Catholic Church likes to have official records of these things. If it was all kind of 'informal' and there is no way to validate what actually happen, they might ask you for a 'conditional baptism' just in case. Talk to your priest about it. I'm not the arbiter either.