I am 19 years old and I have a receding hairline. Should I go in for a FUE? (Photo)

That is not a hair loss because of ongoing process of androgenetic alopecia but  a simple juvenile type maturing of frontal hair line.  That is seen almost every young boys almost between 16-21 that have a very rounded hairline without recession in the corners.  Recession in the corners is a sign of mature pattern male frontal hair line.

It's difficult for any 19 year old to understand why a hair transplant is not advisable. But it's not. A young man who starts losing hair at 19 is likely to develop significang balding later in life. Options to prevent further loss need to be considered right now (finasteride and minoxidil) as well as a plan for how hair transplantation can be used in the future (assuming you don't have miniaturization in the donor area). Transplanting grafts up front in the temples might sound like a good idea at age 19 but will not look good at age 30. You need to find a specialist who can maximize your density and appearance over the next 60-75 years. Transplanting the frontal hairline is likely not part of that plan.