It's possible to have a thyroid issue with normal numbers, but what you've posted, so far, doesn't indicate hyperthyroidism; if anything, the numbers appear to lean toward hypo, but we need to know the reference range for the Free T4, as ranges vary lab to lab and have to come from your own report.
Did you have a Free T3 test done? Free T3 is the hormone that's used by every cell in the body and correlates best with symptoms. I wouldn't rule anything out, without a Free T3 test.
Have you had a thyroid ultra sound? Do you know if you have any nodules on you thyroid? One possibility is a nodule that's producing independently of the thyroid. However, one would expect your FT4 levels to be higher than they appear to be.