you cannot find out if someone already claimed your child for any tax benefits (unless that person tells you that they did) without actually filing your return and claiming your child if you are entitled to. If you try to file electronically with your child's social security number and your return is rejected because of the use of the child's number, you will know that someone already used the number. In this case, if you are legally allowed to claim the child, you must file a paper return. The IRS will eventually investigate both claims, but if you have the legal right to claim the child, this will not be your problem.
I'm sorry that I am not familiar with school benefits? Is this through your local public school, or is this something to do with your tax return? I don't know how your school would know who claimed your children on a tax return--this is confidential information. Unless the school means that someone already used your chidren's numbers for the same school benefits...
I would suggest contacting legal aid in your area to see if anyone can advise you on this matter---It does not seem right that your school should deny you benefits because someone fraudulently claimed your children on a tax return.
In the meantime, you may want to call the IRS to explain the situation 1-800-829-1040, (be prepared for long hold times). And you can follow this procedure for reporting fraud:
How to Report Suspected Tax Fraud Activity
Suspected tax fraud can be reported to the IRS using IRS Form 3949-A, Information Referral. Form 3949-A is available for download from the IRS Web site at IRS.gov, or by mail by calling 1-800-829-3676. The completed form or a letter detailing the alleged fraudulent activity should be addressed to the Internal Revenue Service, Fresno, CA 93888. The mailing should include specific information about who is being reported, the activity being reported, how the activity became known, when the alleged violation took place, the amount of money involved and any other information that might be helpful in an investigation. The person filing the report is not required to self-identify, although it is helpful to do so. The identity of the person filing the report can be kept confidential. The person may also be entitled to a reward.