It sounds like he is trying to get your attention. Try to spend time with him as well as the baby. Praise him for appropriate behavior. Be firm on harmful behavior. You need to protect your daughter and yourself! Since your son refuses to go to time out, pick him up and carry him there. If he gets out, put him back in.
Include your son in activities that will make him a Big Helper or Mommy's Helper. Make him feel included. He could choose a diaper for his sister. He could choose her outfit for the day. If she spits up, maybe he can grab a towel or a burp cloth. Thank him and praise him for his help. When nursing, have special activities that he can do that only come out during this time. Since my daughter loved books, I read books while nursing the baby. That way she still had one-on-one time with me. The baby just happened to be there! : ) One of my friends used an ABC floor puzzle. When her oldest son put in the right letter, she would tell him a story using that letter.
When your daughter is napping, try to spend some time just with your son. Do an art project, cook, play outside, play games. Of course you do need a nap during one of your daughter's naps, so you can relax, rest, and not be grumpy for the rest of the day. (I know, I have trouble from being grumpy, too!) Hopefully your daughter is still taking 2 naps so the morning nap your can spend with your son and the afternoon nap you can rest while your son is napping or "having quiet time". My soon to be 5 year old has "quiet time" where she plays quietly in her room in the afternoon. During my youngest's afternoon nap, I get to rest, too!
Do you have books about being an older sibling? Find some. Your local library should have a good collection. (I ransacked my local library 2 months before my baby was due to get as many books as I could for my daughter.) You can also find some good ones through Amazon if you looking for books to own. There's one by Joanna Cole called I'm a Big Brother. Marc Brown also has one called Arthur's Baby. We have the video copy of Arthur's baby where it also included D.W.'s version of the same story. There is also real kids talking about their younger siblings.
When my baby was little (under 2 months), she "gave" a couple of presents to her older sister for being a "great big sister". You may want to try something similar with your son. It was extra special at the time since it came from the baby. Since you are having behavior problems, you may only do it when he has a streak of appropriate behavior toward your daughter. We did the presents when my baby recieved a present and my oldest didn't. We didn't want our oldest to feel left out. 3 year olds are very aware of presents!
Likewise, before my baby was born, I went shopping with my daughter. She choose an outfit for the baby to come home in. Since my daughter has a lovie, she choose one for the baby (I grabbed 2). Both of my daughters love their little blankets. 2 years later, my oldest daughter still remembers choosing the blanket for her sister. My youngest has to take her blanket everywhere! Maybe your son could choose something special for your daugher?
My children are about the same amount of age difference. My oldest was 2 3/4 when her sister was born. While I didn't have the extent of your problems, my husband and I still had to deal with the jealousy. Our kids are now almost 5 years old and 2 years old and they love spending time together.
Good luck!