I don't know your dance instructor or your studio. I can only share with you my experience with those that I have known.
Are you competing with your instructor as pro/am couple or is your instructor trying to convince you to do so?
Is your instructor an independent who rents time and space at a studio or is your instructor affiliated with your studio?
If the answer to the first question is "no" and your instructor is an independent then there is a possibility that your instructor might help you.
Otherwise, it is highly unlikely that you're going to get help because the instructor and the studio have a financial incentive to keep you from finding a partner.
This website has a partner-location feature. I've had one contact that appeared to be successful at first but ultimately turned out to be unsatisfactory.
There are websites that provide a more sophisticated service but they tend to charge fees that aren't cheap.
Have you tried contacting your local USA Dance chapter (
USA Dance Chapter Locator)? Even if they don't provide any kind of service, you can still attend their dance parties and meet potential partners.
If you have plenty of money then a dance-partner website might be OK. Put "ballroom dance partner" in your search engine and see what pops up. It's not ethical for a user to put the name of one on this message board.
You may want to list your location in another post. Another user may be able to help you better than I can.
Good luck to you. Finding a partner is tough. It took me years to do so.

jj