Hi and sorry you have this.
Colitis is caused by many things. It depends on what type of infection you have whether or not it is contagious. So if you have a type that is viral such as one caused by norovirus or rotavirus you could have a contagious type or a bacterial one like Clostridium difficile, Salmonella or Shigella pr Ecoli that has a toxin (not all strains have it). So you need to find out which one by having the doctor do some lab tests or telling you which one you have. The main thing is washing your hands well after using the toilet. Don't cook for others unless you are very diligent about washing your hands and not getting any body fluids on the food, and don't share utensils or towels and so forth unless you have either been cured of it or been treated and are clear of it. You should ask your doctor for the details. They can usually do a stool culture to check for these things.
Hope this helps.