It was inconvenient for me to hold mine all the time, too, but I made a commitment to meet his needs. His needs happened to include feeling comfortable and secure while seeing the world at the same level as his parents. Mine wanted to sit up and see what was going on from the time that we brought him home, so I gave him what was HIS need. I adjusted my routine to include him. There is no way that I would not consider this a basic need of his. At this age, wants and needs are the same, and helping them to meet those needs is built into the foundation of what makes them feel secure. Some babies can't wait to get out and stay on the other side of the room from their mothers. Some are different. It's our job to know and meet our children's individual needs. They are not all the same kid.
If you need to put her down, you should put her close to you--where she can see you and feel your energy. Talking to her while she is not on your person will help to transition her to self-soothing, not just putting her down and walking away. Put her down for a bit at a time; don't let her cry for too long. Talk to her pretty much the whole time. Let her know that you are still with her even if you are not holding her. You can't expect her to just figure it out.
I agree that you should tell the older kids that you used to hold them, too. While you're holding the baby, be engaged with your older kids so they don't feel neglected. Sorry to pile on, but having multiple children does not minimize their individual needs.
Also, if your holding her does not bother you fibromyalgically--?--then you should be able to find a sling that works. Maybe you were using the wrong one.