I've had my nipples pierced for a few decades. Don't bother trying to hide them because they don't really stand out. Depending on the jewelry you're wearing, of course. I wear simple captive bead rings and no one has ever noticed them through my clothing.
Happy to answer any questions about long-term nipple piercings, if anyone has questions.
Got mine done in '97, and have the same results. I usually wear tshirts, nothing tight but nothing thick either. Everyone I HAVE shown them to was taken completely by surprise and had no idea. I have full rings, I've heard those generally stand out more than barbells, although pulling my shirt tight I can only barely see the lump for the ball so maybe if OP got hardware with really large balls they might be noticeable?