Sort of. I was mid-20s when I found out my aunt was my half-sister. Didn't see her often, but had seen her every few years since I was a baby, so I did know her, and suddenly it was a whole different relationship.
For me, the thing that changed most was my whole understanding of my place in the family, and the trust - if my parents, grandparents, aunts and uncles had all kept this from me for so many years, when I had never had any hint of it, what else could they be hiding? Who could I trust? So for me, that was the most difficult thing to handle.
Your background sounds different, but it could be the whole situation stirs up other thoughts and feelings that are more challenging than the "mere" fact of having a sibling you didn't know about. Only you can work that out, but counselling could help with that. I think it also makes a difference if your Mum or her Dad are still alive, and if either knows you have contact, because then there's a whole load of questions about do you want them to know you know and so on.
Meanwhile, with actually meeting - it should be okay to sat, "I'm not ready to meet, I need more time." Take time to think things through. There isn't a right or wrong answer, but don't rush it if you're not sure. And if it takes weeks, or months or years or never, so be it.
Take care - it's a very confusing time.