So I am trying to defrost some frozen fish using running water, but I do not have a bag to place the fish in. If I just put the fish directly into running water without a bag and thaw it this way, will I die or get very sick?
Fill a clean bowl with cold water. Place in sink. Place fish in bowl under the tap. Turn on cold water so that it slowly trickles into the bowl. This is safe in the short term, or just until the fish is thawed. Of course, a firmer fleshed fish will handle this better than, say, a skate wing or some thin flounder. A plastic bag is basically irrelevant for safety. It will not keep you from getting sick if the fish remains in the danger zone for enough time...that is, unless your fish is floating in contaminated water, which is probably unlikely in your situation.