Congrats on your new position. Hope you are liking it so far. You pretty much hit the nail on the head- it takes time.
When I first started using T-system as an RN I found it a mess and blessing all at once. Now, I have come to love T-system because it is very well laid out. A recommendation I can make to assist you in faster triage is to type the medication names, dosing and frequency rather than clicking and clicking- such as, Metoprolol 25mg BID. I find this approach saves much time of looking up at the screen and down on the paper the information is written on. You can also expedite your entry by focusing on only entering what you need to. If you are concerned of getting the info in for the provider to see, if the provider even looks at your notes, enter only the C/C, pain, vitals, PMH and medications- that is all they really care about. Social history, assessment, and interventions can be added later if your busy with the late entry or manual clock entry feature. I use the following process when I'm getting my butt kicked- prepare the gown, turn on and ready the monitor, pull out all IV equipment and have pen and paper ready for EMS report. As report shouldn't take more than 2minutes at most, immediately use the following time to undress, place on monitor, dress and IV your patient. This can all be done in 10minutes with preparation for EKG. If your patient is a tough stick and can wait a few minutes, enter your info and come back for blood- literally
Orders are a big deal because all ER stuff is *STAT*, but that does not mean each order carries the same level of urgency. You mentioned you had a NSTEMI, resp distress/COPD and pneumonia. Use your nursing judgement to pick your most urgent. I'm assuming the NSTEMI was "stabilized" since she/he could be transferred. The NSTEMI is of priority, but can wait if stable. The pneumonia person will probably get placed on the monitor, blood and cultures gathered, given antipyretics if applicable, and placed on abx, xrayed, CT'd, and admitted. O2, antipyretics and abx are the most beneficial thing for this patient. Get blood, give tylenol, and wait for abx to come up. This person can wait also. I would probably focused all my efforts on the respiratory distress person and worried about getting back to others when my resp distress was "stable."
Hope that helps,