I’ve got sores on the back of my tongue and I can hardly taste anything, what could it be?

Had Hot tea? Sores on tongue & lack of taste is usually secondary to a thermal burn of the tongue & mucosal tissue of the mouth from drinking a very hot tea or coffee. If not, then Canker sores sometime can be accompanied by poor taste or lack of. A medication side effect can mimic these signs also. A more serious condition is called giant cell arteritis. If it persists must see primary care doctor.
Tongue Sores. There are couple of possibilities : herpetic ulcers, hand-foot-mouth disease, traumatic ulcers, aphthous ulcers, thrush to mention few of them. Please discuss your symptoms in detail with your physician.
Viral Infection. You are describing a possible viral infection by coxsackie virus. This infection can cause Herpangina which can cause sores on the tonsillar pillars. I would see a Physician for evaluation to confirm this is nothing more serious.