If your employer fired you, you should file for unemployment. It sounds like you would probably be eligible for benefits, but if your employer contests your claim for some reason, you should seriously consider hiring a local employment attorney to help you pursue your claim.
Bottom line - there is no foreseeable harm to filing for benefits and filing is the only way to get your benefits and answer your question.
This answer is provided for guidance only. DO NOT rely on it as legal advice. We DO NOT have an attorney-client relationship. You should contact an attorney in your area for a one-on-one consultation before pursuing any action or making any decisions.
Yes. It sounds as though 1) you were terminated; 2) your employer does not accuse you of misconduct; and 3) is looking for a person who would be a better "fit." Based on the facts that you've provided above (and so long as the employer reports the same thing to the Employment Security Dept that they stated to you), I believe that you will be able to collect unemployment benefits. If you have any trouble collecting benefits or are denied at the first level, feel free to give me a call. Good luck.
This does not constitute legal advice. You should consult an attorney who can assess the facts of your case and discuss your legal rights and obligations.