Ah, yes, the old "experience required" conundrum. I think there's a possiblity that the experience you've accrued in your current job could be "spun". After all, you're involved in administering and monitoring conscious sedation. You're using many of the sedative and anaesthetic drugs that we use, and are already familiar with their effects and side effects. You also have some understanding of airway management. There is a LOT more to the PICU job than that, but it's a good start! So edit your resume to put some emphasis on that part of your role so that it really catches their eye. Depending on what types of patients the PICU you're looking at admits, that should at least get you an interview. And if you can get an interview, you should be able to sell yourself. Be able to explain how what you're doing now will help you perform well in a PICU (read some of the other threads on this forum) and how your experience provides you with the ability to remain calm under fire. (Airway emergencies, plummeting blood pressure, bradycardia, bleeding, you know.) Refresh your knowledge of growth and development before the interview so that you can handle the inevitable "patient/family interactions" questions. (With kids it isn't always about what you tell them but how you say it.) And do a little reading on family-centred care.
There are many PICUs that hire people with no ICU experience (mine hires nurses without nursing experience!) and the ones that they hire are the ones who can make the interviewer believe they can be taught the job and that have solid skills.