It has to be your decision, but it was a CPN that suggested the 5-HTP to me when I had to come off the Citalopram because of an allergen in the new recipe, but I couldn't be without it now.
It's very sensible that your MH team don't want you to take it while you're still taking the ADs... my team didn't even mention it while I was on the Citalopram, but since stopping it and getting the Citalopram out of my system, it really has saved my life.
I was on the Citalopram for about 20 years and it didn't help me at all and my MH team didn't believe me so I had to keep taking it and living with the suicidal ideation and attempts. Right from the very first pill of the 5-HTP I haven't been that low at all... as soon as I feel my mood plummeting, I pop a 5-HTP and within minutes my mood has lifted and I'm back to being the person that I should be again.
You know you better than anyone - be honest with your team but please do NOT take ADs at the same time as 5-HTP.