Is this normal???

I am really bad at knowing when a relationship just isn’t good and need some advice.

So this is a friend of mine. We are both moms and our babies are a few months apart. She has been kind and good to me, but I’m noticing some things that I don’t think are healthy. First, if we are ever at an event together, she has to be right by my side the whole time and doesn’t like it when I talk to my other friends or pay less attention to her. Next, if we aren’t next to each other, she is staring at me where ever she is. To the point of turning around when I was rows behind her. She complains all the time that she wants to make more friends, but isn’t interested in when I try to get her to talk with my other really awesome mom friends. She is always over stressed to the point of tears about something and always has to tell me about it, but when I have problems she is not around. She doesn’t ask me how I am or what’s going on in my life. She compares our babies and tries to find things wrong with mine in comparison to hers. When she asks for advice or seems overwhelmed and I offer something to help, she brushes me off or tells me she is going to continue doing what she is doing because she is fine. She had lied to me on more than one occasion on some big things. She will have these huge problems that cause stress for weeks where she can’t function, but then she is fine and I don’t hear about them ever again. We went out together recently and she asked if there is anything in her life that I am jealous of, I told her no because I feel we have very similar lives and she looked legitimately disappointed….. I don’t feel like I can be honest with her or really rely on her….she says all the time I’m her best friend, the best friend she has ever had, and she needs me…I feel this is hard for my mental health, but don’t feel like I can walk away easily. She can be so kind and caring and seems to genuinely care for me…..but I don’t know. Thoughts? Advice?