It is important to try to discover whether they knew about the pregnancy since the fact they provided you with a false reason for your termination does raise the suspicion of discrimination based on something and pregnancy is protected. So if they knew that you were pregnant, that would typically give rise to a claim for which you should file a complaint with the state fair employment and housing commission alleging pregnancy discrimination.
If you are unable to discover whether they knew you were pregnant, then you would not normally have recourse against the employer since you would be an employee at will and they could terminate you for any reason.
You should apply for unemployment benefits though since it does not appear you were terminated for good cause.
I would not turn in your resignation. Since this was such a short employment, you could omit it from your work history and if you discover they knew you were pregnant, turning in a resignation could hurt your case.
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