The way I understand what you wrote is:
The order is:
Tylenol #3 0600-1200-1800-2400 -- a scheduled med
Tylenol Plain Q6 hours PRN
You gave a PRN Tylenol at 0300.
Am I correct so far?
If so, the answer is yes. The scheduled 0600 Tylenol #3 should be given.
I would guess this is for pain control. And the Plain Tylenol is for minor breakthrough discomfort?
The next time you could give a PRN Tylenol in this scenario is at 0900. And then, yes, you would give the 1200 scheduled dose of Tylenol #3.
You usually have another nurse to consult with until you are comfortable and gain more experience and confidence.. Also, in the hospital, there is usually a pharmacist to ask his opinion. And lastly, you can always call & ask the doctor...... (I wouldn't do it in the middle of the night).
The doc likes to see his scheduled meds given as he ordered them. If there is doubt, hold on the PRN and give the scheduled. As far as Tylenol is concerned, it is a handy thing to know the maximum mg. a person should take a day, so you don't exceed it. Tylenol is liver toxic. Many docs with toddlers and young children say they won't even have it in their house....if I didn't get the scenario correct, repost it, and I will re-reply.
Hang in there.............