I'm not keen on mineral oil or petro jelly being used on me either, though i do think sometimes it can be hard to avoid it.
My dad has some red tiger balm and also some himani navratna oil that he uses on his sore joints, he said the navratna oil works best so far, but it contains some mineral oil.....though unlike tiger balm it's not the only base as it contains sesame oil too.
Navratna oil gets rave reviews on mouthshut.com though i can't say for myself that i've found it to work as i don't really use it. If there isn't an Indian grocers near you and you want to read more info about it then the ingredients are listed on spicesofindia.co.uk.
Blue ease cream is meant to be very good too, but it contains emu oil so wouldn't be suitable for vegetarians. Dog oil also has it's fans but i can't remember what's in that.....though i'm sure it's not actually made from dogs.....i think it got it's name from originally being used on race dogs.
HTH