Why has your carp fish developed a red mouth and red spot on fin?

The fish is ulcerating because its water is foul. The Basic rules for keeping fish are. :- 1 inch of fish needs at least 1 gallon of water.:- Every fish tank needs a permanently running cycled filter. :'- Every fish tank needs to have at least 50% of its water changed every week. Fail in any of the above and I can guarantee you will always have sick or sickening fish. Observe the basics and you and your fish stand a chance of success.