Lavender oil can be a good thing for aftercare, though it’s not fat based. It still gets through skin anyways, so that’s just a minor detail 
I made a first-aid oil mixture consisting of lavender oil, rose oil and immortelle oil in a bit of hempseed oil - this is really nice for slightly bitchy piercings (not during healing time), pimples, bruises or anything that looks red and annoying. I wouldn’t rely on it instead of going to a doc, but it can be a nice support.
Really good thing! I bought some of those (relatively expensive) probiotics after I had to take a round of antibiotics, and they definitely helped - after that, I found out that the kefir I make at home contains a lot (like, A LOT) more probiotics…
To get back to the problem itself - yes, keeping it still might be really important. Like others already said, the implant is really close to the knuckle, so it might be cutting the pocket from the inside, and that leads to problems… if you manage to keep it, take good care of it - and a special little advice, don’t let your hands get really cold. If skin gets tighter, like after a long walk in the snow, the “cutting” effect might get worse.