I had one baby I could breast feed easily and one I couldn't. I supplemented the one I couldn't. It was fine. He's actually my child with zero allergies and I'd describe overall as healthier. My son that was exclusively breast fed has a lot of allergies and gets sick easier and it has always been that way. So, if you can pump and get enough milk, go for it. Otherwise, formula is pretty darn good these days. I will tell you that my son that we supplemented with bottle (and I did both breast milk in the bottle but hated pumping so we switched to formula) as well as breast fed weaned earlier than my other son.
I also had those lumps occasionally. My doctor told me to massage them a bit. I did. And that got better.
Hang in there mama. It's a beautiful thing to have this time with your baby. :>))
I had a lot of help from a breastfeeding expert from the hospital where I had my baby. Is someone like that available to you? You're supposed to squish your breast into a shape like a fat hamburger, and tickle the baby's mouth with your nipple, and when he opens his mouth, pretty much cram as much of the hamburger into his mouth as you can. Not just the nipple. That method is kind of counter-intuitive, since women tend to think the baby should be given just the tip of the breast, but really you put in a lot more of the breast than you would expect once babe opens his mouth. He will adjust how much he wants, and that way can get a good latch.
The lump is probably milk, and you do need to keep expressing assiduously if he won't drink directly, so you won't get mastitis. Soaking in a bath on all fours with your breasts in the water can also help. But really, the best way to prevent blocked ducts is for your baby to drink your breasts dry each time. They also get the valuable "hind milk" that way.
Good luck to you, please call your doc and see if a breastfeeding advisor is available to you. It makes a world of difference.