Always assess the patient, not the machinery. If pulse ox is 84%, ask them to take a few really deep breaths; some people have occasional bouts of apnea that can make their pulse ox low for a minute, but once they snap to and take a couple of good breaths, they're back up in the 90s. Also move the pulse ox to another finger, preferably on the other hand; sometimes the equipment just doesn't work right on some fingers. If still at 84%, then for the love of all that is holy, of course put some oxygen on!!! Even if the patient has the worst COPD you've ever heard of, put that oxygen on and tell them to breath and breath deeply!!! (O2 tx is bad for COPDers over the long haul, but in the short run, if their sats stay in the mid to low 80s then they are going to be dead, which is also not good for them
). As soon as you get the O2 on the patient and they are breathing deeply, call to the desk, tell them Mrs. Jones has a sat of 84, could then please call the primary nurse to the room. Once the patient is stabilized, then yes, get a doctor's order. Oxygen is considered a drug and you need to have some sort of order to administer it. Any acute care facility should have a policy on this (many responders have commented already about common standing orders), so check out what the policy is for the facility you are at this semester, and make a habit of knowing it wherever you have clinicals in the future.
You did the right thing by getting the patient O2. Your instructor was right that you should also have gotten an order, but the correct chronology was O2 first, order second. Your instructor should have used it as a teaching opportunity, not a reprimand. You did good!!!