The first thing to do is to speak up and let your brother and sister know as clearly as possible what you and your mom would like them to do.
And at some point, siblings have to accept that the care-giving burden isn't evenly shared, and it's never going to be fair. In my experience, caregiver duties almost always end up falling to one of the siblings more than to the others, either because they live closer, have a more flexible job, or maybe just because they're more naturally suited to care giving. Often one child is simply better at it -- calmer, less easily upset, more confident giving medications -- while others are uncomfortable and shy away from it. You have to work through it, because if you don't, resentment builds up to the point that the siblings turn on each other, and then you've lost that support system.
But that doesn't mean your siblings are off the hook. Think of ways they can help out -- then ask them. Maybe a sibling who lives further away could take over paying the bills, or dealing with medical insurance claims. Or ask them how they think they can contribute; they may have ideas you haven't thought of.
You might say, "Mom has chemo treatments once a week and I need someone to take her every other week." Or you might ask one of them to come over and cook for her one evening a week. You need to delegate, but once you do, it's important to let go. You have to accept that they won't do it like you would, and that's okay. One woman in the support group I run kept complaining that her brother never helped, but when he finally did come over and cook, she complained that he made what she felt were unhealthy meal choices. We just laughed and told her, "If someone else comes in to help, they won't do it like you do it, and that has to be okay. If you ask someone to help and then criticize the way they do it, they're not going to want to help out again."