Dialogue in college essay? how to?

“There’s bad people out there, mi amor.” My mom warned me as she held my head to her chest. I nodded. She lifted my chin up and I pulled away from her embrace. As my eyes met hers, she insisted “Don’t you ever let anyone make you do something you don’t want to do.”. She reached for my hands and inquired “We’ve talked about periods, I gave you the book, remember?”. Bulging my eyes at her, “Yes. It’s in my suitcase.” I swayed my arms back and forth anxiously. "Promise you’ll be a good girl? -“I promise.”. She gave me her blessing and sent me off with hope in her eyes. That was the last conversation I had with my mother before I moved to Venezuela with my father. That was the voice I’d remember for the next four years.

Hi everyone, the text above is the first paragraph of my college essay draft. Is this the right way to include a conversation in my essay? Is it too much dialogue? I just feel it’s important as I’m writing about my mom being a motivation for me, as she has been in unfortunate situations and I lived through them with her.
Any input you have I’ll take into consideration.
Thank you so much

also the prompt is the following
Some students have a background or story that is so central to their identity that they believe their application would be incomplete without it. If this sounds like you, then please share your story.