More than 3 weeks ago I have had a sore throat. 12 days ago they did a strep culture and it came back type B, and I was on amoxicillin, but it didn't help at all. Is there a reason?

Have recheck. Persistent sore throat can have many causes. Post nasal drip from allergies or a sinus infection; sore throat due to reflux which can often be silent; viral infections, and other causes. See your provider again if the throat does not improve. Happy healing.
Virus or allergy? Probably the antibiotic didn't work because you have had a viral infection or allergy. Group B strep (GBS) is a normal bacteria that usually doesn't cause symptoms. It probably was appropriate and cautious for your doctor to treat you with amoxicillin when the culture showed GBS, but only as a precaution. Your sore throat probably will continue to gradually improve. Re-check w/ doc if it doesn't.