This can be the throat infection
which is causing severe sore throat
and you are not able to open your mouth.
As you told the you are taking antibitics for the conjuctivitis and this sore throat can be the continuation of the infection down into your throat.
I would suggest you to consult your doctor and after examination and requirement and if the severity of sore throat is very high you may require some oral antibitics and other medications.
I the mean time I would suggest you to start doing warm saline gargiling 2-3 times in a day. This will certainly help in relieving the sore throat. And also continue your medication for the conjunctivitis
Thanks and take care.