Is your employer required to pay you for after hours functions?

All hours worked MUST be paid, that is Federal Law.

Any hours in excess of 40 hours in One Week, are over time.

If you contact (on-line) your state Labour Department, Wage & Hour Division you should get it straightened out.

https://www.twc.texas.gov/jobseekers/texas-payday-...

No they are not required to pay you

You are not required to attend however not attending  might be hazardous to your career

If she requires you to be there, she has to pay you.  Here's the fun part:  When you bring this up, you get fired! 

If you are a non-exempt employee (paid by the hour) your employer does have to pay you for attending REQUIRED after hour functions.  If you are an exempt employee (paid on salary), your employer does not have to pay you.

If you think your employer owes you for last year's BBQ be prepared to prove you were required.  If you think you are owed for the previous years, think again. That will not occur.

Your "rights" are governed by company policy.

I never went to the chili cook off but my co-worker did who named me Chef. I should have made my own Chili and went to the chili cook off. My chili is hot but too tomatoey, said a Marine. Off hours and off the clock, I had to go to the employee recognition banquet to get a ruby pin. I quit before I got the emerald pin. Bogus Bonus, The Hospital Administrator thrust his wife upon me at the employee recognition banquet and walked away.

It sound like you need to find another job.  Forcing this issue will likely lead her to find some other reason(s) to fire you or deny promotions and raises.

If you “have” to attend these after-hours functions, you have to be paid.