Perfectly fine for the tenses to change like this. The case that leaps to mind off the top of my head is The Catcher in the Rye, with its famous opening:
If you really want to hear about it, the first thing you'll probably want to know is where I was born, and what my lousy childhood was like, and how my parents were occupied and all before they had me, and all that David Copperfield kind of crap, but I don't feel like going into it, if you want to know the truth. In the first place, that stuff bores me, and in the second place, my parents would have about two hemorrhages apiece if I told anything pretty personal about them.
Note that this is all in present tense, while the main body of the narrative is in past tense. There are two time frames in the book, narrative time referring to when Holden is telling his tale to his unknown interlocutor and story time referring to the actual events of the story, e.g.,
I was trying to feel some kind of good-bye. I mean I’ve left schools and places I didn’t even know I was leaving them. I hate that. I don’t care if it’s a sad good-bye or a bad good-bye, but when I leave a place I like to know I’m leaving it. If you don’t you feel even worse.
Some other examples that spring to mind would include Paul Zindel’s The Pigman where, picking quotes from the Goodreads page,¹ we have one of the two first-person narrators talking about the other in narrative time:
She thinks she knows everything that goes on inside me, and she doesn’t know a thing. What did she want from me – to tell the truth all the time? To run around saying it did matter to me that I live in a world where you can grow old and be alone and have to get down on your hands and knees and beg for friends? A place where people just sort of forget about you because you get a little old and your mind‘s a bit senile or silly? Did she think that didn’t bother me underneath?
and in story time:
“Be yourself! Be individualistic!” he called out after me. “But for God’s sake get your hair cut. You look like an oddball.”
Most of all, though, to be a good writer, you need to be a good reader. It would behoove you to spend some time reading books that are written in this sort of format where there is a self-conscious narration. The two books I’ve mentioned are rather old,² but they’re also pretty short, and not a bad starting point.
⸻
I last read the book 40-some years ago and never owned it, so these aren’t necessarily the best examples, but they’ll do the job.
If you were thinking wow, this guy’s coming up with a lot of old books and remembering stuff he read decades ago, yeah, that’s part of it, but also books you read when you young tend to imprint themselves much more strongly than those you read when you’re older. Odds are that most people here might be able to remember a lot more specific language etc. from books they read as 12-year-olds than books they read last year.
Unless they’re 13.
