I'm poly. Gf says she is but... isn't?

So, my gf told me before we dated that she was polyamorous. I am too but am also fine with a monogamous relationship if I really like the person, so I was fine with it!

One day, I met a girl I really liked and let my girlfriend know (this was months after I started dating my girlfriend)...

She. Flipped.

She changed her mind and caused issues between the two of us, causing me to stop talking to the girl for a while. She said it was because she was suddenly uncomfortable and didn't want to go on a dating site again because people were mean to her. I told her she could wait until she found someone, but she said she couldn't. As if she had to be dating someone else before I could??

Fast forward: She meets another girl and then decides surprise!! I can be poly now!! Like...what??? I had to tell the other girl I wasn't in a poly relationship because she changed her mind...but now that she has someone else, it's fine??

She seems to be the type that only believes she can be poly and not me. What do I do?? Is this relationship even worth keeping? I've been with her for a long time and really like her, but I'm so tired of this... I'm scared of being with someone else because she may just change her mind again.