First of all, they really don't look too bad.
im wondering if theres any other possible way to get rid of the puffiness
Unfortunately, there really is no good way to get the puffiness down. You can modify your diet slightly, which can help, and you can try to work out and increase your testosterone levels a little bit - although I have seen that some people on this board it strangley has the opposite result for them.
Yours are very similar to mine, except for I have much larger and more defined pectorals. I have found that developing my upper chest (inclined bench and similar such excerizes that work the upper part) has really helped with making the nipples look less conspicuous. Do they stick out in a tee shirt as well?