Different articles will say that there are no negative side effects:
"Toxicity, side effects, interactions, and contraindications
No side effects or interactions are known with oral administration of glutathione. There are no known signs of toxicity from glutathione. GSH and other thiols may be sensitive to redox-active minerals, and care should be taken to omit these from therapeutic preparations." That is taken from
Glutathione | amino acid health benefits, dietary sources, side effects
I also read that one should not take Glutathione is one has diabetes or kidney disease. Are you making sure you are drinking enough water?
It is always best to go back to the doctor who prescribed l-glutathione to you. Beter safe and to know exactly what is going on than wonder what if.
Good luck.