Are we a good match?

Hello, I was born in Indonesia on October 18th 1989.
I am currently engaged to a woman, whose birthday is on October 7th 1990.
We have been together for almost 3 years, but our relationship is on the rocks at the moment. If we face conflicts of our egos, I feel like it is very difficult to find solutions and sometimes I feel like we are in different waves in the relationship.
Are we a good match, and is it okay to proceed to a more serious commitment with her?
And if the relationship is worth fighting for, what do we have to do to improve our relationship and make the bond between us tighter?

Thank you.