Allowing Military Exemptions, Recognizing Individual Concerns About New Shots Act of 2023 or the AMERICANS Act This bill prohibits the Department of Defense (DOD) from issuing any COVID-19 vaccine mandate as a replacement for the rescinded vaccine mandate of August 24, 2021, unless the mandate is expressly authorized by Congress. The bill also provides that DOD must establish an application process for remedies for members of the Armed Forces who were discharged or subject to adverse action under the rescinded mandate. Any administrative discharge of a member on the sole basis of a failure to receive a COVID-19 vaccine must be categorized as an honorable discharge, and DOD is prohibited from taking any adverse action against such a member for that reason. Under the bill, DOD must try to retain unvaccinated members and provide such members with professional development, promotion and leadership opportunities, and consideration equal to that of their peers. Additionally, DOD may only consider the COVID-19 vaccination status of members in making certain decisions (e.g., deployments in countries where it is the law) and must establish a process to provide exemptions to certain members for such decisions. This bill applies to all members of the Armed Forces, regardless of whether they sought an accommodation to any DOD COVID-19 vaccination policy.