Yes. This.
Call her back, listen to her, and just reflect her emotion back. You don’t need to fix it, or correct anything that sounds outrageous to you. That’s not your role. Your role is to tolerate the big emotion, and say things like “That sounds so scary” and “I’m so sorry you have to do this” and maybe at the end of the call, “Is there something you can do right now that would be comforting?” Big mood swings are normal.
[/someone currently in chemo]
I’m sorry you had a rough time. Just for some perspective, I was able to work and exercise through eight rounds of chemo and 30-odd radiation treatments. YMMV, of course. If your sister is suffering side effects, tell her to talk to her doctor. There may be some way to treat it.
Where’s Allen Funt?
Where’s Ashton Kutcher?
Where’s my coat?
Thanks to everyone who has provided useful advice. Spoke to my sister briefly last night, and fortunately her panic has subsided somewhat.
I have a richly deserved (and understandably annoying) reputation as the “Mr. Spock” in my family. Sometimes it’s a blessing, as it helped considerably getting though my own recent bout with prostate cancer, and sometimes it’s a curse, like now. Will just try to do the best I can.
It’s all anyone can ask of you. Now tell your sister that, if you haven’t already 
Just remind her of that and be a sponge for her frustrations and emotions. As said upthread, don’t try to fix anything, instead reflect her sentiments back to show you hear her and are sympathizing as much as you can.
The chemo is cyclical. My friend was getting treatment just every 3 weeks, but the time between was some rollercoaster of feeling OK and feeling like crap. She lost a bunch of weight and her doctor told her to try to gain some back. Then when everything was over, she started Tomoxifen and now she’s gained 50 pounds in a year.
But it’s not just chemo. It’s I have cancer. My friend didn’t handle the news well and though she had a slow one that her oncologist said may have already been there for years, she didn’t tell anyone for a couple of months, and didn’t start treatment for another four months after diagnosis. She did some things that were very uncharacteristic of her because of not talking about it, and one of those ended up with her getting fired. So yes, people all handle the news differently, and carry on with their lives sometimes forever changed even if/when they are declared cancer-free. My friend will never be the same, the treatment and emotional toll aged her 10 years.
Take your cues from your sister on what she needs from you. One thing to keep in mind is that there will probably be times when she’s so tired of dealing with cancer that she wants to talk about something else - anything else. If you find her in this mood, you can talk to her about family matters, or friends, or movies, or whatever you usually talk to her about. You can help her maintain a sense of normalcy.
Let me second this. I know when I was going through chemo I got tired of people asking how I was doing in somber, caring tones. It’s not that I didn’t appreciate the concern, I did, deeply. It’s that cancer and chemo take over your life; you can’t help but think about it all the time and…and sometimes you just want a break from all of that. You just want to have a normal conversation about everyday things and not think about how you’re doing and what you’re going through.
So yeah, sometimes just ring her and ask in a normal tone of voice, “Hey, what’s up?” and let the conversation go wherever.
Depends. Between blood and in-laws, my family is apparently trying to colect 'em all types of cancer, and the latest three treatments (for three different types) have all had very different reactions.
Talk with your brother in law; you and him know your sister a lot better than I do, but I can tell you that some of my relatives (and of their closest) liked to get calls on the day they had treatment while others hated it. One liked being called while waiting for it (distracted her) but not after. You can’t be there physically but modern comunications provide multiple ways to be a long-distance shoulder.