Um, I have one of those, and yeah, you probably shouldn't squeeze them... but I do. Some have milk come out and one has the little solid but come out. I've been doing it since I was 4 months pg, and Ruby is now 8 months plus, so I don't think it's a blocked milk duct. Generally they really really hurt, and your boob goes red and hot and it would hurt to squeeze it.
I leaked earlier for my second pg. but not as much as you! You might be leaking if you are doing things like squeezing bits on your boobs as this is all stimulation!