Pretty sure I’m pregnant

I had my last period on October 29th, had unprotected sex on the 17th of November. He pulled out but we were intoxicated…heavily. My period is now 6 days late. I’ve never missed a period, however I’m 36 almost 37. Thinking I could just be going through peri menopause. I’m currently on vacation with family and I don’t have any privacy to take a test. Anyone has a similar experience or have thoughts?