Babs is... less than thrilled that you're sick.
It's not that she's upset at you. She's not. It's not your fault. Sickness happens. She's more than willing to take care of you. That's not the issue.
Look, it's just she's got a lot on her plate, and it's been kind of hard to shuffle stuff around so she can take care of you properly. Oracle's system never sleeps, and she has obligations as Barbara Gordon to handle as well, and it's just been a lot. That's not on you. You're the priority here. The fact that she's getting stressed out trying to juggle everything is on her.
...It doesn't help that she's starting to seriously worry about you. She's starting to let other obligations slide a little bit, because she doesn't want to leave you alone for long. Heck she skipped going to the Clocktower during everyone's patrols last night and just managed things from her laptop and phone, because she didn't want to leave you unattended all night, and didn't want to make you make that trip with her just so you could sleep on her couch there, you know?
And Babs knows logically that you can handle a couple hours on your own. Under normal circumstances she wouldn't think twice about it, obviously. But now she's just... worried something might go wrong? What if you need something? What if your cough or your fever gets worse? What if you try to get up to grab a drink or go to the bathroom or something and collapse? She wants eyes on you, is what it comes down to, and if that means she's stressing a bit about how to get other things done without leaving you unattended, that's on her. And if she's rushing home from work at the end of the day rather than taking her time and stopping for a nice coffee like she usually would, even though she just texted with you to check in an hour ago, that's on her too.
Maybe she's mother henning a bit, but she'd say these circumstances justify it a bit, yeah? "you? I'm home," she calls as she maneuvers herself through the front door and bumps it shut behind her.