You can certainly file an action in the small claims court, but it is not clear whether you have any good claims here. If you relied on someone's promise to your determent you may be able to ask the court for a remedy to make you whole. But if for example it was not reasonable of you to purchase the ticket at that time and should have waited for approval or something like that then you may not have a good claim here.
You can always just sue in the SCC who you believe to be the correct party and if they disagree and believe someone is responsible they are free to either join them as a defendant or seek an indemnity against them.
You will not require a lawyer in SCC.
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It's unfortunate that you're out the $360 cancellation fee, but it's not clear who's to blame. Regardless, to answer your "should I sue" question, my advice would be no. You'd have to draft a small claims complaint, pay the filing fee, take time off from work and show up to court, maybe sit through two hours of a docket call, and try and convince a judge that you're owed $360. If the judge hears all the facts and thinks it was a baseless lawsuit, you could end up paying the defendant for his/her time and expense. If you're right and you win, you still have to figure out how to collect the judgment through a bank levy, wage garnishment, negotiations, etc. You'll also probably make an enemy forever in the process. I'm not trying to say that your time isn't worth it, but I'm saying that you'll spend a lot of time and expend a lot of effort to pursue your claim when you could be using the time to invest in an endeavor that makes you more than $360.
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The unfortunate situation is that your costs to sue, especially if you are not successful, could far outweigh your loss at this time.
The costs of filing (even a small claims) nowadays is not cheap -- not unreasonable, but still around $100 in most jurisdictions in Indiana. By the time you calculate your time to prepare the paperwork, prepare for the hearing, attend the hearing and all that comes with that, you may want to charge this one off as a "learning experience."
Oral contracts (he said and she said) are some of the most difficult "contracts" to prove a breach.