Is it normal for me to hold a grudge against my bully?

it is normal but it is not healthy. When you hold a grudge, it is like holding a rotten meat. It is only hurting yourself and the longer you hold it, the stinkier it becomes. So you need to learn to let go and move on. The bully didn't even know that you are holding a grudge against him, he wouldn't even remember about you or the past. So there is no point of holding a grudge. Instead, learn to forgive. I know it is hard and impossible but at least learn to forget. don't get obsessed by it

Feeling anger and resentment is a totally normal reaction when we have dealt with being mistreated, humiliated or violated. However something as holding grudges might not be healthy and helpful to you in this context, as it might prevent you from letting go of that thing and focus on living in the present. If that is the case acknowledging your emotions, allowing yourself to feel them and then practicing forgiveness little by little could help. What is most important though is that you talk to someone about it and address the bullying to stop it in case it is still going on.