Good Morning K., Congratulations on your future little princess.
Sometimes Binky's and sleeping go hand in hand. They use them to self sooth. Just like a favorite blankie. Our eldest son told his 3 1/2 yr old he was throwing Woobie away cause he was a big boy now. Well Nana ( me ) stepped in and let him know it had to be Corbin's decision not to sleep with woobie anymore. And that is all he does with Woobie, sleeps with it. I told him I didn't even have to take your bottle away, you decided at 19 mo. you didn't want it anymore and threw it away yourself. Went completely to a cup. You carried your blankie everywhere with you until you were almost 4 then you gave it up on your own. * we still have woobie * ;)
Our 5 Gr children each had something near and dear to them and all at one time or another gave them up willingly. Zane our youngest gave up his Binky and uses his thumb to suck when tired, gave up his bottle and uses a sippy. He turned one in Oct.
Each child is different of course, his Binky may be helping him right now more then you know since he is ill. I have never had Mono, so I don't know all of the symptoms and how it is spread other then the normal stuff, kissing, drinking from same cup etc..
If he seems to only wake up when he is looking for Binky you might try on of the Binky attachments they have. He can find it quicker and go back to sleep sooner.
Just some thoughts, some mama's start by clipping the end off the Binky's, so they aren't as satisfying. Some have giving them to the Binky Angels to send off with a balloon for the new baby's in heaven.
God Bless K., hope you get some great advice from the other mama's out there.
K. Nana of 5