hi jennifer, My lo is 9 months and was exactly the same, soon established going 3-4 hours in the night but the days could often be hourly. If i fed him every hour sometimes by the afternoon he would go a whole three hours, then back to hourly again. It went on like that for months but as he was my only child and i was getting sleep at night i didnt mind too much! Can't imagine how hard it must be with 2 children to think about too though.
The HV would say that all this stimulation is important for milk supply - at 3 weeks, that's still being established, and giving your baby a dummy could intefere with that as well as stop her getting all she needs. However, i know it must be really hard so maybe getting one without relying on it too much (only when you absolutely have to) might be the best decision.
I think the sling sounds a better idea though, if your bubba wants closeness, leaving your hands free, you dont say how old yout older two are but maybe you could have a discussion with them about how important it is the baby feeds and make them part of things. Also maybe have some nice skin to skin time with your baby while they are at school and a cheeky snooze yourself (lol) just to give your calm and reassure your LO.
I know at 3 weeks it feels like a long dark tunnel, constant feeding that will never be over, and if you've bottle fed before it can be very tempting to go over to bottle feeding again as you know he will take a bottle and sleep! However, once bf is off the ground its the most beautiful, bonding experience and you wont ever want it to be over once you get to the easier bit. You are doing a fantastic job x