Most websites either organises or schedule posts but do not do both and none of them are free. 

Buffer.com is a website that you can plan and publish content that drives meaningful engagement and growth for your brand. The starting price is $15 a month for 1 user, $65 a month for 2 users, and $99 a month for larger teams with 6 users. 

Airtable.com is a website that allows you to keep all your projects organised. It does have a free option but it is very limited with options to work with. Then it starts at $10 per user per month, $20 per user per month and the unlimited version you get a special quote when you sign up.  

Hootsuite.com is an all-in-one social media scheduling, monitoring, and analytics. Starting prices are $29 a month with 1 user, team profile is $129 a month with 3 users, and prices just keep going up from there. 

Loomy.com is either $25 a month with 3 users if you pay annually, if not it is $34 a month. 

School organisations have low budgets on marketing material.