In her philosophy she expressed that there is no such thing as altruism, that everyone exists for their own selfish needs.
This is incorrect. She thinks that altruism is a negative thing rather than a positive thing.
And her definition of "selfish" has to do with "rational self-interest."
She argues that the ultimate moral value, for each human individual, is his or her own well-being. Since selfishness (as she understands it) is serious, rational, principled concern with one's own well-being, it turns out to be a prerequisite for the attainment of the ultimate moral value. For this reason, Rand believes that selfishness is a virtue.
...
Rand understands, though, that the popular usage of the word "selfish" is different from the meaning she ascribes to it. Many people use the adjective "selfish" to describe regard for one's own welfare to the disregard of the well-being of others.
...
For her, the truly selfish person is a self-respecting, self-supporting human being who neither sacrifices others to himself nor sacrifices himself to others.
Read more: https://atlassociety.org/commentary/commentary-blog/4141-virtue-of-selfishness