You don't need to see a breast specialist or have surgery.
That is probably (I am 99.9% sure) something called the tail of Spence, and it is part of your milk duct system. It's located all the way up in your armpit. It's not a lymph node or anything like that. It's the end of the milk ducts. Some women have them all the way up like that.
Same thing happened to me when I had Colton. I got a funny and sorta painful lump in my armpit. I didn't feel engorged anywhere else in my breast tissue, but I asked here what it might be, wondering if it was a lymph node. One of the leaders suggested tail of Spence, and she was right. I can't remember when it went away. It was probably about the time my milk supply evened out.
You can google it. I don't have links up right now.
Regarding oversupply. . . do not pump. Just feed the baby. Yeah, you will be uncomfortable between feedings. You can hand express enough to stay comfortable, but if you pump, you signal your body to make more milk. If it stays there, your supply will even out a whole lot faster. I speak from experience. I got really bad advice with #1 and pumped after nursing, and just a few weeks in, I could pump 8 ounces after feeding the baby, at each feeding, and he nursed every hour. My second baby was a lot more content to just nurse every 3 hours, and it was hard to not pump since I knew I had so much milk, but within just 2 weeks, my supply had evened out nicely. I still had a lot, and I leaked a lot, but it was nothing as awful as the first time around.
Hang in there, and it will all work out.