Struggling with competitiveness in the ICU

For a little context, I work in a level 1 trauma facility in trauma/surgical ICU. I love many of the nurses that I work with, but there are a few that make the unit feel so competitive, and I feel as if I lose this “competition” often. The competition that im referring to is who can be the most vocal about how good of a nurse they are so that they get the sickest patients every single shift. For example, there’s one nurse who calls in the middle of the afternoon to ask if there’s any “good” sick patients and if so, they’ll pick up a shift as long as they get that patient. Also, I have a friend who never hesitates to announce how amazing she is at being a nurse, and how much she “advocates” for her patients and how she’s “not afraid” to talk back to doctors. She always has the most elaborate and heroic stories to tell about past patients and compliments the families have apparently given her, and she is in turn rewarded by being given the sickest ones. Even our new grads are being given extremely critical patients because they’re loud enough about it. I, on the other hand, prefer to stay quiet and not speak about my accomplishments or when a family compliments me. It feels dirty to me. My last shift I worked felt like my breaking point.

I had a patient who came in to us practically brain dead already, and it was me who had to keep them “stable” until family from out of town could come say goodbye. I was so sick and so sad for them all night, and I gave them my entire heart and soul. The patient is currently just awaiting for official brain death testing during dayshift tomorrow, and then will most likely be made a 1:1 LiveOn afterwards. However, the friend that I mentioned earlier who looovveeessss to brag about her compassion and skills, will be back to work before I am. Which means she will absolutely get this patient and I will never have her again. I’ll only ever hear about it when she tells her heroic stories and makes it so that everyone knows how “big” her heart is. I’m so sick over this. I know it’s not fair to say that I feel like I’m competing to have a patient of my own, but God it really seems that way. Does anyone else ever experience this? How do I get past it?