You are perfectly entitled to say how you feel, presumably because you feel this relationship is a potential threat? There is also a wide scope as to what is meant by to 'carry on' ?
If your gf has care and consideration for you she would curtail this relationship, if you have explained why it makes you feel uncomfortable. However, it depends to what degree she is 'carrying on', is it casual conversation or meeting up? It can be a big confidence boost to know someone carries the flame for you. But equally if she sees the grass is greener and there are flaws in your relationship with her she might well decamp and find love elsewhere.
None of us 'own' anyone or have the right to possess someone else in any relationship. For true love (& marriage) to flourish with love and laughter each free spirit has an unconditional right to stay together, by choice, never by force, and never by pressure from others.