The EIN is free for the asking. Go to
www.irs.gov
and download form SS-4.
Yes, your PTO could be independent of the district and many, many PTO's are. But, like pals said, it sounds like your administration doesn't want the PTOs to be independent. You could buck that, but the school still has to support your work (think: allowing you to meet in the school, publicize through the school, send notes home with the kids, etc.) in order for your group to be successful, independent or otherwise.
If your PTO members like the idea of being independent, then you should ask the district if they'd support your PTO getting its own EIN and putting the $$ in its own account. If the money goes into a district-controlled account, you give up your independence. That's no necessarily a bad thing, but you should agree to that arrangement with full knowledge. Whatever you do, get that money out of the personal account.
And if you do become independent, you don't need to apply for formal federal tax-exempt status until your group has at least $5,000 in gross income for 3 straight years. From the sound of it, you're not to that point yet.