At the low cost clinic you can get shots and other tests. They do a basic exam on your pet.
Yes, they'll do a basic health check when they do vaccines, but they won't take long and they won't do any diagnostics (they might do felv testing, but no in-depth tests). If you know your kitty has an issue, you'll need to take it to a full-service vet. If they find something in the exam that needs further testing, they will tell you to go to a full service vet.
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