Yes, I have had similar experiences. It has been a long time since I nursed my kids but I remember is vividly. My daughter was my second child and from the moment she was born she wanted to nurse all the time. My breasts became to sore but I stuck it out for about 6 months. When I tried to slow the nursing down my milk was just flowing like crazy from so much nursing. My breast became engorged and very painful, and eventually rock like. The doctor told me that she could use a prescription but first advised me to pack my breasts in ice. Which I did. It eventually worked.
Any lump should be checked out by your doctor, though, just to rule out anything serious.