Nursing pads are already very discreet, especially if you use the disposable ones. Disposable nipple pads are thinner than reusable ones, but with the right bra, neither will show through your clothing.
If you’re worried about how the pads are showing through your bras now, try on some bras with thicker padding.
It’s easy to carry these around in your purse and then change them out in a bathroom without anyone knowing what you’re doing. Overall, they won’t be noticeable to anyone but you.