How long have you been doing this? I ask because I'm a huge introvert and small talk is so painful for me. My med-surg experience was so busy that I could not have chit-chatted with my patients even if I wanted to (sad, I know).
I'm in an ICU now and I have a mix of rapid recovery post-ops that I'm extubating and keeping til the morning, and sedated ventilated patients. if my patients are awake enough to be talking to me (and stable), I can be more helpful to my coworkers so there's less awkward alone time in my patient's room.
Keep in mind the hospital is a scary foreign place for most patients. Small talk is a good distraction for them and helps make human connection. Over time, you will probably feel more comfortable. I think patients and families can sense when conversation is forced or if we are not being genuine, so often if conversation doesn't flow, I'm not afraid to be present and be silent. With those kinds of patients, to increase the sense of my presence, I'd try to do my charting in the room, and even charting for other stuff I need to catch up on, in which I'll say something like "I'm just going to do some charting in the computer here, don't mind me but don't feel like you're interrupting me if you need anything."
I've been with peds a few times, which I found more difficult to interact with parents. I felt 100x more awkward. Idk about your hospital or patient type but parents are around at night just as much.
In summary, I'd try to deal with your introversion and finding ways to make it work with your nursing style, not just avoiding people as much as possible. Even if that would be so much easier