Is my female friend jealous of me?

My female friend always:
- Brags about handsome and attractive men chasing her but she ends up rejecting them.
- Brags about how intelligent she is.
- Brags about how many friends she has.
- Only talks about herself and her life. Never listens to mine or offers advice when I invite her to.
- Brags about all the guys checking her out.

All these things are unwarranted. I don't mind her occasionally saying these things and supporting her, but it's on a constant basis. It comprises of 80% of our conversation. Also, she knows that I like military men and when she found out I'm with a military man, she starts jumping in and showing off about the military men she has rejected (no photos, no proof whatsoever).

Things to mention is that I'm reasonably attractive, tall and successful. I'm a student pilot and one of the better ones at flight school. She knows this but I never brag about my achievements to her or the attention I get from both genders. What should I do about her self centered nature?
Is my female friend jealous of me?
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