AITA for skipping friends birthday?

I have a friend of 2 years who didn’t congratulate me on my birthday once, but once it’s her birthday we go to restaurants and I gift her something. And I’m not sure if I’m being pity or what.

So on my birthday in October last year we were just friends for 6 months and I don’t have any social media to indicate that it’s my birthday so she didn’t congratulate me which I ignored and went to her birthday party in December and gave her a gift. This year she remembered that my birthday passed 2 weeks later and just asked why I didn’t tell her and she said let’s than meet for a coffee on the weekend with a friend of ours and they will congratulate me? I didn’t remind them about it cause it felt weird to celebrate my birthday a month later even though we leave literally 10 minutes away from each other.

So now her birthday comes around in a week and she calls me to come to the nice restaurant and I don’t know what to say. I don’t feel comfortable coming empty handed but also coming there and gifting her something feels not fair to myself.

I know I didn’t throw a party for them to come, but still feel weird. AITA for wanting to skip her dinner and how do I approach it? Should I tell her how I feel or just make an excuse and not show up?