I am 1 year and 2 months older than my sister. My sister still has on her arm tiny marks from my upper teeth. I had bitten her for no reason at all, she was just a baby (and so was I). My mother told me that I was incredibly jealous, and she also said that one of the things she regrets is not giving me attention when new babies came. I always had to be "a big girl". I was a big girl from the day I was 1 year and 2 months.
My suggestion is that you try to arrange special time to be with her. Just her, not the baby. And make it regular and often. But don´t slap her, it really is not necessary. It does not solve anything.