It could still be strep throat. Sometimes you will need a different antibiotic. The lumps on your neck are most likely lymph nodes that have swelled up due to this throat infection. I don't think you should be worried right now that this is something more serious. But I think you do need to go back to the doctor and get re-tested for strep. There is another possibility and that is that there are some people who are carriers of strep and if you test them, they will test positive for strep but the strep doesn't cause any symptoms for them.   If you are one of these carriers, it is possible that your sore throat is due to a viral infection and not to strep. In other words, the strep was just hanging out in your throat (probably for a long time) and not causing any symptoms. If this is so, then an antibiotic will not clear this up and it should get better on its own within 2 weeks. I would ask the doctor about this possibility at your appointment. Because of the swollen lymph nodes the doc will probably want to change you to another antibiotic anyway.
To help it get better, you can try a warm, salt water gargle. Chloraseptic throat spray can help relieve some of the pain. So can Tylenol or Motrin. Warm compresses may help reduce some of the swollen glands in the neck.

If you have further questions, let me know.
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