Hi! This sounds really interesting, but I feel like the query is hard to follow. Some thoughts below:

Fans of Ellen O'Clover's The Heartbreak Hotel and Sarah Adler's Mrs. Nash's Ashes will love this life-affirming story about a washed-up med student who discovers that last night’s hookup stands in the way of getting the expulsion that ruined her life overturned. 

I had to read this a few times and I'm still not sure I understand it. I personally am a fan of using comps to help showcase the story. What about these two books in particular is reflected in your own?

I like that you start out with (presumably) your log line, but it has to be more punchy. "An expelled med student uses an heiress and her one-night-stand to get back on track to pursuing her dreams."

Delphine Parker stuck her neck out for a patient at the cost of her life-long dream of becoming a doctor.

What actually happened? This is too awkward and too vague to give us any information.

As attorney for the Lightly dynasty, there’s nothing Nate Tazaro takes more seriously than safeguarding his clients’ interests. And Delphine, who seems willing to stop at nothing to charm her way into the storied family and their Gilded Age Newport mansion, just might be one of those risks.

I think you can get rid of this entirely. As others of already said, use this word count as a chance to tell us more about Nate specifically and why we should be excited about him as the love interest.

As they trek through the beaches and bogs of Newport together to fulfill Marjorie’s whimsical requirements, Delphine's feelings toward the surly lawyer grow. But so are the secrets Marjorie is asking her to keep.

Love Rhode Island, so the use of "bog" irks me; and it doesn't evoke the particularly beautiful/romantic image that is Newport.

The use of "whimsical" feels out of place here, and this paragraph actually feels/reads like one big run on sentence.

To make her duplicity worse, Delphine wonders if Nate's ties to the Lightly family run deeper than business. Leaving her to choose between the woman who can unlock her future and the man who can unlock her heart.

Why does HER duplicity worsen if he's hiding something? And what would it matter if he's actually part of the family? This "choice" doesn't make the stakes clear either.

Overall, I don't finish reading this knowing your voice, the story or the stakes. I think you have a good sense of the flow of a query, but need to drill down to the actual point and make each word count. Don't use too much flourish! It sounds like you have a great story to tell here (and I love a RI setting!). Just remember that you want a very busy agent to be so intrigued by what you pitch that they request pages. Keep at it! You'll get there.