I just cleaned a fish tank with a dead fish in it and I have open wounds on my hands and now arm is tingling

Do you have a question ?

If you are concerned that you may have gotten an infection then you need to see a doctor. Sadly no one can diagnose online, not even a doctor.

Take a sample of the water in the tank (if you have a sample of the water you removed), when you see your doctor. If there is an infection then testing that water will help determine what it is and how to treat it.

It is always best not to come in contact with the water in a fish tank when cleaning it. If you cannot avoid contact, wear rubber gloves.

Alty is correct. For the same reason children should be allowed to handle turtles, or anything similar, without wearing gloves. They carry diseases we could not even contemplate, including salmonella poisoning.

If you can give it some thought, use your common sense, and realize what would be in that old dirty water; fecal matter and rotten food from the fish that were in it. And of course organic matter from the dead fish.

If you had open wounds at the time of coming in contact with the water, you stand a good chance of having a serious infection that would be quite contagious and you should go to a walk in clinic, or see your doctor immediately.