I understand your concern. Fever need not be present with every case of Tonsilitis. The redness, pain and lump on swallowing are all symptoms of Tonsilitis and pharyngitis which you seem to have. The pain under your jaw could be due to inflamed lymph nodes which occur in the presence of infection.
Since yo do not have a fever and Penicillin doesn't seem to help, the cause of this infection is most likely viral. You do not have to worry as this usually resolves on its own but takes time.
For a quicker recovery, I suggest that you follow these measures.
1.You need to continue salt water gargling, at least 3 times daily. An alternative to this would be a 3% hydrogen peroxide mouthwash or gargle. You have to dilute the 3% solution with an equal volume of water; swish around in the mouth over the affected area for at least 1 minute and then expel. Use this up to 4 times/day (after meals and at bedtime)
2. In addition you can take an OTC like Ibuprofen 400 mg, twice a day with food, for 5 days.
With these measures, you can obtain relief.