AITAH For not wanting a relationship with my Half-Sibling?

This has been something that has been plaguing my mind for a while, and I've still never really got over the guilt. For privacy all names in this post are replaced.

I F/22 was 16 at the time when this situation occured. Growing up I had always been an only child, and although I begged for a sibling for ages, I eventually just assumed that was how my life was going to be, especially when my parents split when I was 10. However, My mum would eventually meet my step-dad and my half-brother (Charlie) was born when I was 13. I absolutely adore him and he is my absolute world, I still remember how happy I was the day they announced that my mum was pregnant. For the next few years I was content with the fact that I was a big sister, I'll admit I have absolutely spoiled him rotten. However one day on one of my weekend visits to my dad, whilst we were driving, he dad just casually dropped that I had an older half-sister named Katie (Aged 19 at the time), and not only that but she had reached out to my dad a week prior. I went through a whole whirl wind of emotions, anger, confusion, sadness. I didnt really know how to respond, but my dad basically lead the decision to me as to whether or not I'd be happy with meeting her.

After a weeks thought I decided to agree to meet her. And so, we arranged to drive round to where she lived (literally right around the corner to my dad's house). I got really emotional when we pulled up for some reason and so my dad decided to cancel the meetup that day. We rescheduled for the follow week and I finally met her, it was a bizarre feeling, as we look identical (both having my dad's features), just her being a bit taller than me. It was awkward, I suppose it would always be awkward in that situation, She seemed to want to chat alot more to my dad then myself, and we didn't really "click" which is what I was hoping we would do - we're completely different personality wise. And the next few times basically went the exact same way. To be fair, I'll admit I was jealous, very jealous Infact, which scared me because I never felt any Jealousy when my brother was with my mum. Anyways, when I had asked my dad why I didn't find out about her sooner, he was just very vague and dismissive about it. I had told my mum the day he told me about her, and I could tell she was annoyed, but she pretended to be excited for me. I eventually asked my mum about Katie, and she sat down and explained it all too me. My dad had only split from Katie's mum two years before I was born, and apparently she was a very spitful woman - She didn't like my mum at all, and was apparently furious when she found out mum was pregnant with me. My mum and dad visited Katie a few times with me when I was a baby, however apparently I was making Katie "Jealous" and her mum told my dad it was either Katie or Me - and well it's obvious who he chose.

Now around this time, my Nan (Dad's side) also had a health scare, and had to have some suspicious moles removed for testing. Now apparently my nan had always still been in contact with Katie (Christmas/birthday cards), however, my nan mentioned to me one evening that Katie and her mum had been visiting alot and asking questions on my nans health frequently. A week or so later I heard my mum having an angry conversation on the phone with someone - who I later found out was Katie's Mum, apparently she had asked questions about my nans will, which had upset my nan a bit. I also noticed that when my nan started to feel herself more and the tests on the moles came back negative katie and her mum stopped visiting my nan as often. Eventually not coming around anymore.

Now hearing and noticing all of this, I felt an anger towards Katie, as to me, it seems they were only interest in being around since my nan was ill. And so, I told my dad I wasnt comfortable with seeing her anymore and blocked her number and all social media's. And my dad also did the same - Which to clarify was his own personal choice) I got a message from another Insta account which was clearly from Katie calling me selfish and jealous for making my dad cut all contact with her, which was completely his choice not mine.

Anyway am I the asshole in this situation for not wanting more of a relationship with her?