Hi Anon, sorry it took so long to get back to you!
About your questions ... yes it is OK to take L-Tryptophan if it is already part of your multi-vitamin/mineral etc. There are no such thing as an amino acid to avoid. All amino acids are naturally occuring in our food, especially meat, as these compounds are the building blocks of protein. The only danger would be in over-supplementation.
The daily recommended dosage is 250mg to 500mg per day, but it is possible to take up to 1500mg per day (for not more than 2 weeks at a time, although this might be too much to start with -- best to start with a smaller dosage and work up to an amount that you feel comfortable with, and which produces results - but not more than 1500mg PER DAY!!!).
There are some drug interactions with L-Tryptophan, particularly SSRIs and MAOIs, but I would suggest that you look up drug interactions with any other drugs you are currently taking just to make sure.
Hope this helps,
All the best,
Anthea