No, for a couple of different reasons:

1. Mammals diverged from reptiles approximately 325 million years ago during the Carboniferous period.

So your potential dinosaur heritage has nothing to do with where you live now.

Carboniferous Earth:

https://en.m.wikipedia.org/wiki/Carboniferous

2. Dinosaurs wouldn’t evolve until 230 million years ago. About 100 million years after mammals had already split off from the reptile family tree.

So there’s no chance you have any dinosaur DNA. Our family and their famlly evolved long after the split had already happened.

Your heritage at that (extremely long span of ) time might be a small shrew/rat/squirrel like creature that scuttled around at the time of large dinosaurs. Probably hiding from the the small to medium sized dinos. Too small to be of note to the large ones. Adaptable enough to survive the mass extinction - maybe small, agile, mobile, omnivorous and so on.

This is a contender for an early primate - maybe - I think the fossil record is a lot less complete and harder to interpret for smaller creatures. https://en.wikipedia.org/wiki/Purgatorius

Of course the dinos changed a lot over that time - as would the mammals. I think Purgatorius is from near the K-T extinction.

There were other larger mammmals around but probably none much bigger than a wolf / lynx/ capybara type thing. I think those types are considered less likely to have evolved into primates and also some might have evolved and re-evolved into something else many millions of years before the K-T extinction.

That depends—are you a bird?

Sure, why not.

By adoption maybe… how adventurous was somebody’s grannysaurus and their special friend?