I found out the name of that essential oil. It's called helichrysum. I guess if the antibiotics aren't working, it might be a consideration. Keep in mind, I've never used it myself, I have no idea if it's safe for rabbits, and I have no idea if it would even help. I just saw the effects if seemed to have on my nieces cut, and thought it pretty remarkable. If you do try it, you need to make sure to get it from a reputable company. You're in the UK, right? I'm not sure what you would have available there.
Anyways, whatever you end up doing to help your bun, I really hope he pulls through ok.