My baby’s throat is red, she’s been coughing, and she sounds hoarse, should I call the doctor?

Maybe. Sore throats, coughing and congestion are usually caused by viruses...Which go away on their own. Well appearing infants without fever do not need to see their pediatrician. If your infant has a fever, is breathing quickly, is not eating or drinking, or generally doesn't look well, then you should definitely call your doctor.
Yes if. Yes, if she has a fever or does not seem to be improving in 1-2 days.