Based on your description of your public support, you are probably registered as a public charity under either section 509(a)(1) or 509(a)(2), and you should be able to endorse the check without worry.

When you originally applied for recognition of exemption as a 501(c)(3) charitable organization, you also had to give the IRS information on whether you should be classified as a public charity or a private foundation.  The Tax Code provides that all 501(c)(3) charities shall be classified as private foundations, unless they show that they qualify as public charities under section 509(a). 

Section 509(a)(1) includes churches, hospitals, educational institutions and other groups that receive broad public support (not counting program service revenue) from gifts, grants and contributions.  A local United Way is an example of these organizations. Section 509(a)(2) includes organizations that receive broad public support from gifts, grants, contributions and program service revenue from their charitable programs.  A nursing home is an example of this type of organization.  Private foundations receive their new income (other than investment income) almost entirely from a very small number of supporters, often a single individual, family or corporation.  The Gates Foundation is an example of a private foundation. 

Your original recognition of exemption letter from the IRS will tell you whether you were classified as a public charity under 509(a)(1) or 509(a)(2), and you have to check the proper box on Schedule A to the Form 990 or 990-EZ.  You can’t be “only” a 501(c)(3).  All 501(c)(3)s are further classified either as public charities under section 509(a), or as private foundations.  You are almost certainly a public charity.  You would know if you are a private foundation.