Is the grow light on a timer? Plants need dark time just as humans need to sleep. Put the plant under light only 12 hours a day. I could not identify your plant and it may be one that prefers a lower light level. The grow light may be too close or too strong. Try entering the name of the plant followed by .edu, no spaces. You may find cultural advice from research done by state extension services. 
The brown area below the green leaves makes me skeptical that the plant will recover. You may get new growth from the roots.