Is this relationship worth saving?

So me and my girlfriend been together for 3 years. And she is an insecure person. I love her very much and I know she loves me but the problem is every time I talk about working out or when I get promoted with my job, she always gets upset saying I’m moving up in life and I’m going to leave her for someone better. And when she gets in these moods she’s very mean and nasty but then apologizes after. I tried talking to her about it and she keeps doing it. I’m tired of feeling like it’s wrong to succeed and wrong to improve myself. Is this a relationship I should try to make work? As I said I love her very much but it seems nothing I do is good enough for her.

Is this relationship worth saving?
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