You are right that sows can become pregnant at 3 week of age. Most likely your sow is pregnant.

It's really your choice whether you want to separate or neuter. Neutering can be dangerous if you don't have a cavy knowledgeable vet. I've gotten two pigs neutered and they both were fine. Teresa of Cavy Spirit's has had countless done and more then not they were fine.

Also if you get your male neutered you will need to keep him away from the female for at least 3 weeks. Even though he will be neutered he may still be fertile for at LEAST 3 weeks.

I see nothing wrong with neutering but make sure you have a very good vet doing the procedure. You also may want to think if you female is pregnant -what are you going to do if the baby is male?

Good luck on whatever you decided.