What causes the arms and legs to be purple spotted or really red?

Meningitis. This is a disease which poisons your blood, causing the horrific blotches.
Have you noticed any other symptoms including a stiff neck, very tired, and sometimes feeling very floppy.
If not any of these it may be Septicaemia. The symptoms include, sickness and nausea, tiredness, and being scared of bright lights.
To find out if it is any of these, roll a tumbler along your arms and legs. If the marks fade, it isn't septicaemia , or meningitis. If the marks stay, you may have one of these diseases.
Check for the other symptoms, too, but if you do think you have the disease see your GP - F.A.S.T.

Good Luck.