It's not fuzzy, but a red and black bug that will sting or bite you is a black widow. It is a black spider with a large abdomen and a red hourglass shape on the bottom of the stomach. If bitten, you should see a doctor for medical treatment.
It is the joker bug. Named after the black and red color associated with medieval English court jesters. There are two sub species of this critter. One is the one you refer to, one that stings and another that does not.
it may be a velvet ant, there are about sixty different types of them and are not all that common they, some people think they are wasps but that is probably because they attach themselves to bees and wasps
That bug is called the red velvet ant. It actually hurts a lot when this bug stings. Therefore, the best thing to do is actually to prevent this damage by applying some sunscreen before hand. If you get stung, then apply tea tree oil right away to soothe the burning itch.
The Velvet Ant is red and black with fuzzy legs and often stings. This insect is called the 'cow killer' and can cause pain and swelling with its attacks.