I have been drinking tonic water because I was told that quinine was good for treating inflammation in arthritis, is that true?

Quinidine. Mostly beneficial for spasms and muscle twitching and aches; less likely associated with anti-inflammatory effects.
Kind of. Quinine is related chemically to other compounds (hydroxychloroquine, chloroquine, quinidine) that are refered to as anti-malarials due to their use to treat malaria. The have also been shown to be helpful in some kinds of inflammatory arthritis and are used regularly for that. The most common example is the use of Hydroxychloroquine (plaquenil) in rheumatoid arthritis and lupus.