Forgot to mention that just because levels are in the "normal" range, doesn't mean they're right for you...
Many people find success with just T4 medication, but it has to be dosed properly.
What was the reason for having half your thyroid removed?
Is your doctor testing your thyroid hormone levels regularly? She should be testing Free T3 and Free T4, along with TSH, at regular intervals - preferably, every 6-8 weeks until symptoms have been alleviated.
Since you still have symptoms, I'd say your dosage is not adequate.
If you'll post your most current lab results, we can better tell what testing is being done and help determine what you might need for treatment. Be sure to post reference ranges with all labs, as ranges vary lab to lab and have to come from your own report.