It doesn't matter whether the noise is being made by a 'piece of medical kit' or by a washing machine, or a treadmill, or loud music. It's something that can be resolved, so you need to make an effort to resolve it.
There are multiple options available to you - it's just that you don't particularly want to take those options because each of them will cause some inconvenience to you or your husband. Having a baby brings all sorts of changes and inconveniences and compromises. You had a baby. Your neighbour didn't, so why should she be expected to be the one who suffers or changes her living arrangements?
You could ask your husband to sleep without earplugs and leave the baby in the room. Yes, this might mean that the he's woken, rather than the neighbour, but it is his baby after all.
You could look into a quieter pump. Yes, this might mean that it takes longer for you to express at night, so you lose some more sleep, but it's your baby, not the neighbour's.
You could move the baby upstairs with you. Yes, this might wake the baby, and lead to you losing more sleep but it's your....well, you know where I''m going with this.
You could go upstairs without the baby and take the monitor with you. I'm not sure I see any downside to this one.
You are allowed to leave the room when you have a baby. You don't have to be within touching distance at all times. I co-slept with both of mine, carried them in slings pretty much full time for the first three months or so, breastfed on demand, so I get it. But you have to be sensible about it all, and you can't expect everyone around you to change their lives around to accommodate your parenting choices, beyond the basic consideration that most people extend to parents with young babies.