I worked in an NICU for 20 years. I do know how you feel. While family & friends would tell me how lucky I was to be able to "hold & rock babies all day long", we all know that there is much, much more to it all than that.
An RN from NICU had to attend every delivery, which relieved the L&D nurses from having to care for the baby & could devote all their attention to the mother. While I watched every delivery, I also was anticipating there being an unforeseen problem. Of course, when there was a problem, that also meant way more work!
I don't necessarily think that means that you are burned out, I think you are realizing that your job entails very hard work. If you do feel unsecure in your knowledge of how to handle a problem, take a NRP course or ask questions of co-workers. You may just need more time to feel more secure in your job.
Good luck with whatever you decide.