I started with a sore throat and voice loss now i have a chesty cough and rashes on my chest and back what could it be?

Viral illness: Most likely a viral throat and larynx infection that is causing cough either by vocal cord irritation or progressing to trachea or lungs. Hydrate, use humidifier, rest voice, use honey and dextromethorphin to suppress cough if it is nonproductive. Laryngitis is rarely bacterial. Rash is also probably a viral exanthem.

I agree that the illness is most likely a viral infection, use supportive care and monitor your cough. Watch for worsening, more phlegm, fever and shortness of breath. Often nasal saline rinses are effective in reducing post nasal drip. For soothing your throat, warm liquids, voice rest and a teaspoon of honey may be used. Please follow up with your PCP.