I had/have issues trying to get professional development such as learning a new language or reviewing study guides for an optional certification done, and part of the problem I had was that it always felt overwhelming with all I had to get done otherwise. It was hard to set aside large chunks of time to devote to it, but much more manageable to do smaller windows here and there. Maybe try setting an alarm for a small 15-20min window that you know you have free on a day to help with just setting aside that time to begin with, once or twice a week, and as you get more into the routine you can adjust length of time or frequency
Best piece of advice I could give to anyone is make as much relevant connections as possible and preserve them as best as you can. Jump on every connection possibility as fast and as enthusiastically as you can or just hook in to existing connections between existing connections.
I always viewed wearing multiple hats as proving your worth. Hey look, I can do my job AND others AND do a damn fine job at it all. Personal internal cred.
Thank god they don't make me answer the phone. I volunteered, once. Thankfully, they know better.
Do the job that's in front of you. Exigencies of the service and all that. If it's way out of the pale, then it's good for later anecdotes and additional experience. At Nike my cubicle name tag always got flipped to Batman when I was out running calls, I thought that was droll.