Being right on the joint could further complicate matters. If it was just a slight sliver in the flesh & accessible with a good set of tweezers or sharp blade, I would recommend "go for it" & use a triple-antibiotic initially, and then afterwards Bag Balm as Larry recommended above (really good stuff for the skin). However, since it's on the joint I think you should see a doctor to get it taken care of. If it should get infected & affect the bone in the joint, the infection can spread via the bone marrow throughout the body. Don't mess with it yourself. The doc will no doubt prescribe an antibiotic, perhaps Amoxicillin (???)
Thoughts entering one's mind need not exit one's mouth!
As I age my memory fades .... and that's a load off my mind!
"We Live In The Land Of The Free, Only Because Of The Brave"
“The problems we face today are there because the people who work for a living are outnumbered by those who vote for a living."
"Socialism is a philosophy of failure, the creed of ignorance, and the gospel of envy, its inherent virtue is the equal sharing of misery." Winston Churchill