Does the sentence seem natural?

I'm telling someone about how I got fired from my job, then after that I say:

It was a few days after I had moved into my new apartment, so it couldn't have happened at a worse time.

Does this seem natural?

My doubt is if it's natural to say "it was a few days after..." instead of "it happened a few days after..."?

And if it's natural to say "...after I had moved into..." instead of "...after I moved into..."?