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The answer is essentially yes. To sue in a state court, one needs to have a "cause of action." There are numerous causes of action, such as "breach of contract," "negligence," "fraud," "unjust enrichment," etc., as well as causes of action rooted in statutory law. Every state has their own although they are very similar to each other in every state because they all stem from the same common law. A pleading in Court needs at least one cause of action, although it is not unusual to have more than one.
Here, someone in your situation can sue for negligence and breach of contract.
NEGLIGENCE: Presence of a a duty of care, breach of that duty, and damages to you from that breach.
BREACH OF CONTRACT: Existence of a valid contract, breach of that contract, and damages to you from that breach.
The Court will normally award damages based on actual damages sustained, which may include the ticket, costs, etc, as well as possibly even costs to redo the visa with another agency.
If you tell me what state you are in, and what state the company is in, I can be more specific as to my answer. Thanks!
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