I did a thyroid test and it showed that my free T3 (liothyronine) is high...While my free T4 and TSH is normal. What does it mean to get a high t3 (liothyronine)?

How high? Reference ranges are set so that several percent of folks fall outside on either side. If it's not way-off, and your TSH is normal, and (most important) you feel well, ignore it.