Girlfriend mentioned about a guy who made her 'unable to think properly'. Is this a red flag?

Anonymous
First of all, my girlfriend is very insecure. There was once I did not hold her hand when crossing the road, and she cried for a night, saying that I no longer love her.

Recently, she mentioned that she went out with a guy who is handsome, patient, and caring. They past by and went in to a jewelry shop. According to my girlfriend, the presence of this guy made her unable to think properly and she ended up buying an expensive piece of jewelry, which she will never do (because her finance ability is not so strong yet). At the end, she told me that I have to be careful.

Recently, she casually mentioned that the 3-4 month into a relationship is when people start to cheat. Our relationship is reaching the 4 month mark in a week. And when I playfully asked her: so are you cheating on me? She gave a weird expression, and brush off the conversation.

My girlfriend is very young (21 years old), and this is her first relationship. Whereas I am 29.

Is she telling me that I am not doing good enough to win her and should buck up, or is she hinting that she is still 'playing the field'? Since she is still so young, and exploring, and want to know which is the best guy she could be with.
Girlfriend mentioned about a guy who made her 'unable to think properly'. Is this a red flag?
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