Oh Sveta! That sounds awful. I hope you are feeling better soon.
How about something like this? http://www.amazon.com/Undercov.....B00428ZHRC
A (wonderful, bless her!) experienced mom gave me a set of Lily Padz nipple covers when I had just had my first child. Life changing. The silicone covers seamlessly cover and obscure nipples so that there is no show through. Honestly, I use them anytime a bra isn't feasible and sometimes when I just want the extra modesty protection (cold room, silky top, padded bra alone isn't going to do it). They last for many, many wearings.
Or these? http://shop.nordstrom.com/s/no.....y-personal...
I used something like those for modesty coverage before discovering the silicone covers, and they provide a little more bounce control. Unfortunately, they are expensive when you consider cost per wear.