Hello, welcome and thanks for asking your question. My name is*****'m a Certified Auto Technician with 28+ years experience. I will do my best to assist you. please keep in mind that I may need to ask questions of you before I can answer. When you reply please feel free to add as much detailed information as possible pertaining to your concern.
The symptoms you describe lead me to a possible failure of the Alternator. An internal short can cause the alternator to emit a "Humming or Whining" sound and also cause it to overheat.
If this sounds like your issue, it can easily be tested with a multimeter. If you have access to a volt/ohm meter, test the alternator output directly at the alternator charging terminal and directly at the battery, If charge output is less than 14 volts, likely the alternator has failed and needs to be replaced...
If you need additional information, don't hesitate to ask, I am happy to help as long as necessary to help solve your concern. Remember, a "Positive" Rating will not close this question, You can post a reply here whenever you want, even after rating my answer! .
Keep me posted and let me know if you have any additional questions...