Welcome to FT, Sara.
It sounds to me like you're pursuing an EU261 claim.
If so, two things:
1 - If you're considering doing this through a claims management company, don't. Go to TC directly first. Only if you get rejected and it looks like an either way case should you use a CMC.
2 - I don't know TC's systems personally myself but with all the information you have (flight, date, pax names), they should be able to find your info easily and you shouldn't need to go through any data protection request or pay any fee. Just go to the EU claims team and they will respond to your claim.