Sister-in-law troubles

So last year, my bro-in-law (hubby’s bro) got married & now I am blessed with a sister-in-law. She has quite the reputation. Mutual friends of ours have said that she is all showy when it comes to impressing others, but behind closed doors she’s a total fake. They’ve always said that my bro-in-law could’ve done better. I never let what others get to me... But it seems like now I’ve been given reason to think along with them. Long story short, my mother in law used to hate her, but has come to accept her as family. My sil has done & is doing everything she can to get my mil to like her. On special days my sil will purchase gifts & cake for the celebrant of our family. On my bday she didn’t even greet me even if everyone around her did & even if everyone in our family text thread messaged me. I found it odd that she just didn’t greet me, but she greets our other family members. Am I jumping to conclusions about the way I think she is. Is she trying to compete with me in a petty way? I’ve always been kind to her so I don’t know what the issue is.

Only kind words pls... Thanks in advance for your help & insight.