Is it possible I had a chemical pregnancy last month and didn’t know ?

Last month I had sex right when I was ovulating. I didn’t know it then. We used a withdrawal method. I didn’t even know how to use the calendar method and so didn’t know I was ovulating. Anyway my period came early and lasted 2 days. But everything in me told me I was pregnant 🤔 after doing the math. I had a lot of alcohol so now I’m thinking maybe the alcohol caused it to be chemical ?! Or maybe I’m thinking too much ?