Written by Rabbis Eli Gersten, Yaakov Luban and Moshe Zywica of the Orthodox Union
They are most likely protein spots.
Approximately 20% of brown eggs have protein spots which are only found in the egg white (albumen). Some of the pigment excreted by the chicken to color the shell leaks into the egg white and collects in clumps. These colored clumps are, at times, quite large and have a reddish-brown color. In other cases, the protein spots are just “specks” that look like someone sprinkled red glitter into the egg. Testing of protein spots shows that they contain no blood cells and are blood free!
Rav Belsky, zt”l, ruled that protein spots are halachically permitted and there is no minhag to prohibit them.