You can sue in Small Calims court for up to $7,500, and you can sue on this oral contract, but it'll be harder to prove than if you had a written agreement. Basically you'll to prove the material facts of an enforceable contract, the what, when, where, and how. This means what you agreed to do, and by when, and what the client agreed to pay and by when.
You can use emails, texts, and the payment of your costs to show you did have a contract. Anything you don't have in writing may be disputed, so you'll have to prove that part of your case with your testimony.
If part of your agreement was that the prevailing party would get their legal fees in any dispute, then you can hire a lawyer to help you, even if the lawyer can't appear for you in Small Calims court. If you didn;t agree to that, that's another reason to make sure you have written contracts from now on.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
I agree with my colleagues that small-claims court is appropriate. You might find information at the link below helpful.
Disclaimer: This post does not constitute legal advice and does not establish an attorney-client relationship.