One of the easiest ways to check is to search the
IRS database of charitable organizations
to see if donations to your group are tax deductible. You can also call the IRS and give them your Employer Identification Number and just ask.
Usually if your PTO is already set up, you know it. You are using statement about deductibility of contributions on your materials, you are filing a tax return, getting correspondence from the IRS.
Your organization is probably operating as an unincorporated association. Independent from the school, but not incorporated at the state level or set up as a 501(c)(3) non profit with the IRS.
This is fine as long as your organization doesn't bring in more than $5000 GROSS per year. Once you pass that threshold, the IRS expects you to formalize. Otherwisel, if you aren't a person and you aren't a non-profit, then you are basically just another small business
and should be filing taxes as a small business.
Many, many of us were incorrectly told our PTOs were 501(c)(3)s. This was verbal history passed down by well-meaning folks who didn't understand what that really meant.
Good Luck!
P.S.
and have a tax exempt number
The nine digit identifying number is an EIN (Employer Identification Number), also sometimes called a TIN (Tax Identification Number). It's simple to get. Free. Can be done by mail, phone, or internet.
The IRS can use the EIN to look up your organization, but the number itself has nothing to do with being exempt. It's simply an ID number like people have social security numbers.