You feel what you feel. You have a choice over whether you express your feelings.
There are more of us around than you'd think. I discovered I had a half-sister in my 20s. If she'd been born 4 years later - well, she wouldn't have been, because abortion was legal by then.
I didn’t have a problem with the fact of an extra sister (although my younger sister was furious, that I had forced her to know by telling her - she wasn't given a choice, but neither had I been, and it wasn't knowledge I could have and she not - what if she had layer found out that I had known and not told her?) The thing I struggled with most was trust. Because of the circumstances, it would not have been just my mother who knew, but also my father, my paternal aunt and uncle, my paternal grandparents, as well as obviously my maternal relations. They'd all known this big thing all these years and I had never even had a clue - what else might they have decided not to tell me or even lied about? Over 20 years on, I still struggle to trust people, despite having had a fair bit of counselling.
I think it's quite reasonable to have confused, inconsistent and changing emotions. It is about you, even if it's more about other people. Finding out as an adult that you have a sibling you never knew about can be really upsetting, because it leads you to question all sorts of things in your life and relationships you thought were solid, but now you don't know.
Give yourself time. There''s no right or wrong way to feel, though others may thibk you shoukd react a particular way. One way or another, you do need to adjust to this - you can't change that it has come out - but adjusting may not be quick or easy. Acknowledge your feelings, expect them to change and change again. It's not necessarily going to be easy, but you can get there. Take care.