I think i have an infected hangnail on the left side of my ring finger. it is very red, swollen and quite sore to the touch. can i treat this at home?

Yes, at first: This may be a paronychium (inflammation around the area where the nail meets the finger's tissues). You can try frequent (every several hours) prolonged warm soaks which can bring this to a head and allow drainage. If, however, the redness extends beyond this area, the finger becomes swollen or in any way worse, you should be seen immediately, preferably by a hand surgeon.

Sounds like : An oral antibiotic might be in order....the hanging nail needs to be addressed as well.