It sounds as though you are not improperly classified.  You are a charity and public charity rather than a private foundation.  Gifts to your organization should be deductible for individuals and businesses that itemize their charitable contribution deductions and should be qualifying distributions for private foundations that need to meet their annual distribution requirement.

Organizations that qualify as charities are described in section 501(c)(3) of the Tax Code, as you say you are.  They are classified as “public charities” under Section 509(a) of the Code.  The IRS does not classify as an organization under 509(a) unless it first qualifies as a charity under 501(c)(3).  (See Ready Reference Page: “Calculating Public Support Percentage”)

This information is generally available on the recognition of exemption letter that you received from the IRS when you were first recognized as a charity.  Show it to your potential donor(s).  It will say that you are classified as a 501(c)(3) charity and state the section of the Code under which you are classified as a public charity.

You can also suggest that your potential donor check you out on the IRS website by using the Tax Exempt Organization Search Tool on the Tax Exempt Organization Search page in the Charities and Nonprofits section of the website.  You can search on your organization’s name or your Employer Identification Number.  The search should confirm that you are listed in Publication 78 (the list of exempt organizations) and provide the applicable “Deductibility Code” for donations.  You should be listed as a PC, or public charity, and not as a private foundation.

If your exemption letter was dated after January 1, 2014, you may find a copy of the letter there as well.  You should also be able to find copies of filed Form 990 or 990-EZ tax information returns.  The IRS has recently announced that the Search function will be the primary source of exempt organization data and the solely available direct source of 990 information.  (IRS News Release 2021-250, 12/16/21)