My sister is very cross with me and seems to resent me. Is this a normal reaction?

Your profile says you are caring for someone with dementia... your sister? I think that it would only be natural for her to resent the realities of her life and that you are free to come and go while she is not, I remember years ago when I would take my mom to visit her sister there were a couple of residents who grumbled "how come she gets to leave?" when we went home! It is also normal that all the anger and resentment spills over onto those who are closest to her because we do tend to "let our hair down" amongst family. Add in alzheimer's confusion and there may be times when she forgets her disabilities, she may even distrust you are her sister because in her mind she is living in a different time.

Is this a sudden change in her mental status? If it is, id discuss it with the medical staff at her nursing home, she may be suffering from a UTI, which can bring on beavioral changes in elderly patients.