Proving a transaction is mine As an assignment in a digital security course, a group of 100 students was asked to transfer a small amount in bitcoins to a certain wallet. They promised they'd buy something for us from this money. As a proof that we made the transaction, we've been asked to hand in the transaction id. 

I'm wondering what exactly restricts me of using blockchain.info to search for this wallet address, wait until someone else has made such a transaction, and then just use that transaction id. 

Am I right that merely requesting the transaction id isn't enough here?

Of course, they could notice when two people hand in the same transaction id, but we're in different groups, so they may not notice.
See Is there a way to prove ownership of a transaction?, which suggests using the private key to sign a message. You could send a signed message to your professor with the transaction id. However, since you say you're in different groups, it can still be that someone from another group just uses your transaction id, and doesn't get caught.

I would suggest asking your professor to give everyone a different wallet address to transfer the money to, or to request that everyone signs his transaction id with the private key used for the transaction.