My gut instinct is telling me something is off with her

So this is a lot so I try to keep it short and as interesting as possible.

1. i met A guy at work and we really hit it off. At first it was just him and I.

he told me about a girl that he was seeing before me but they ended up going their separate ways because she decided that she wants to be free and explore her options.

Fed up he begins to date me. She had no interest in him until she found out about me. Upon finding out about me, she suddenly wanted to be back in his life.

she began to do things like popping up at our job to see what I look like, and waiting in the parking lot to see me walk in and out of the building.

I immediately didn’t want anything to do with her just off of that. It was giving me the vibe that she’s mentally unstable.

okay fast forward to when we finally meet up (I wanted to give her a fair chance cause he was excited about it)

it didn’t go well because she said some borderline offensive compliments to me (called me a sexy prostitute)

gave her a second chance and it actually went well. So now here we are in a real relationship.

I still can’t shake that gut feeling that something is off. especially after certain things that have happened since then.

1. she went off on him for asking me for money before asking her.
2. she stated several times that she’s jealous of me for various reasons
3. she’s complained about the way I dress and the way I do my hair, getting in his ear about me shaving when he and I already agreed he didn’t care about me shaving
4. she once even investigated the bed to see if we had sex, sniffing it and feeling if it was wet
5. shes expressed to me that she’s not prepared for him to fall in love with me
6. she bragged to me and laughed about the way that she treated him prior to me entering the picture (about leading him on and playing around with him knowing that he wants to settle down)

there are other more detailed things I can’t include and other things I’ve forgotten about, but I don’t know what to do.