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Can you please take a video? It is impossible to judge what is going on just going by your words.
Please be aware that picking up is generally stressful for piggies; this means that even the slightest obstruction in the small and narrow airways is becoming audible with increased heavier breathing. Guinea pigs don't breath much with their mouths. If you don't hear anything at other times, I would frankly not worry.
The clicking sounds that are serious are clicking with the teeth (generally an expression of pain/overgrowing teeth) or from the lungs (can indicate pneumonia, especially in combination with heavy breathing from diaphragm).