tryptophan is a serotonin pre-cursor, different type of neuro-chemical. i guess some say its like a mild anti-depressant... but.
just because you have the precursor, doesn't mean you'll make the target chemicals in the body (in this case, serotonin in the brain, hopefully not in the gut where it cannot cross the blood brain barrier, and the gut is where most serotonin is created).
but melatonin is produces from a solid light, and lack of light. ie when you see bright light in the morning it stops the meletonin production, in the evening as the sun goes down, our eyes detect this and tell the pituitary gland to stimulate producing melatonin all through the night, until you see bright light again.
serotonin has very very little play in this axis. its called the placebo effect.
edit: need to be very careful with these things, unfortunately most people are on anti-depressants, which affect dopamine and serotonin, and drug interactions can cause real negative side effects. very touch subject.
need to think, why are you lacking serotonin? whats the cause? because that is the solution, real talk.