Too low of calories!!! 1,200 is nothing. She is starving herself, start with tweaking her macro ratios first before messing with estrogen, injecting l-carnitine, etc. No need for that crazy shit when she needs fuel to get thru her work and workouts. 
1,600 cal (low end at best)
40% P
35% C
25% F
I agree that too low of calories, especially for a long time, can impede fat loss.
I had a friend that was eating 700 calories a day, dbl cardio and was not dropping. As soon as she upped the food, she started dropping. The first week after increasing her food, she actually gained like 5 pounds, but then it all started coming off. Her body had been protecting itself aginst starvation and thus holding on to the fat!!
As for the mesotherapy, fat buners, anti-e, it is always healthier to do it naturally.