while it would be nice if they had some personal experience of chronic severe illness i think they will be able to help even if they have not experienced it themselves. the same approaches are generally applicable.
i think it possibly matters more how well your sister connects with them - so don't be afraid to try a few if after a 2-3 sessions she doesn't feel a connection.
people who are depressed and angry are often very resistant to and impatient with therapists - so it might take some perseverance to find one that works for her - but i do think it will be worth the effort.
ref written material - i think the psychology today may have some useful general reading
ie if you search their site with "chronic illness"
https://www.psychologytoday.com/gb/blog/psychoanalysis-30/201103/the-dis-ease-chronic-medical-illness