What signs is he giving you that he has a sore throat? I'm not challenging that he does, just thinking that the way he behaves may give clues to how you might help him.
I would try a tea made with echinachea (it's kind of bitter), a little bit of guava nectar (not honey for a 2 month old), and some slippery elm. Slippery elm bark comes in a powder and is very soothing--and will not in any way harm your baby. It's a food source. You might try it in a bottle, if he takes one, but he may not be willing. Another method is simply using a small teaspoon or baby spoon to spoon little amounts into his mouth.
UPDATE: To respond to those above, I am a long time midwifery intern. I never started a practice of my own because my third daughter came along as I was starting to "catch" babies at births myself rather than just assisting, but I have quite a bit of knowledge of herbs and nutritional methods to care for young babies. I have also used this with my own children quite successfully when they were little (we didn't have guava nectar then, but any natural sweetener that is not honey is fine) This is a very easy and common method for herbalists and naturopaths to use with babies. It is in no way dangerous--for S.M., a little bit of water/tea in the amounts I am suggesting will not interfere in any way with a baby's electrolytes.
What IS dangerous is Tylenol! It contains a liver toxin that in doses just twice what a person should have by weight can and does cause death. If you choose to use an over the counter baby product, make sure it does not contain Tylenol (aceteminophen). Most do, but that does NOT make them safe, and I have read recently that the FDA is finally getting the message on this.
