I've had cold& cough for 3 wks mostly gone but now throat is sore like a muscular sore there's tiny white pin size dots and red streaking what is it?

Get checked: Upper respiratory infections can last up to 1-3 weeks without any adverse effects. However if you have a sore throat, a throat culture must be done to rule out strep throat infection. Redness on the tonsils and white spots (exudate) are signs of a bacterial sore throat and may require antibiotics to treat the infection.

Tonsillitis: From your description it seems you may have Tonsillitis and it may be strep tonsillitis and may need to be treated with antibiotics I suggest you consult your Family Doctor and may need check up and if indicated quick strep test or culture and appropriate therapy with antibiotics if it is strep infection