I EPed and did have mastitis twice and both twice, I ran a fever which increased quickly (e.g. in less than six hours), so I'm hopefully from what you've written that you don't have mastitis yet! It also sounds to me like a plugged duct (inside the breast) and I had those too and, after my first bout with mastitis, I was especially vigilant about trying to get rid of them because I didn't want to risk getting mastitis again. Because my DD couldn't directly breastfeed at all, I couldn't use the baby's chin technique. Here's what helped me:
--heat: warm compresses before and during pumping.
--massaging the lump while pumping, using my thumb and pressing on the lump and pushing toward the nipple.
--just pumping the breast with the lump for a few minutes and altering the suction and speed and seeing if that helped.
--hot showers: I had a hand held sprayer and would put that right near the lump. I did lose a bit of milk that way, so I tried the other techniques first.
I'm sending good thoughts your way!
PS For me, getting rest was always helpful to my pumping and to being able to take care of and enjoy my baby and getting other stuff done, so if I were in your situation, I would probably try the baby chin's technique during the day, but not at night, so that you can keep your nighttime feeding and pumping sessions shorter. That said, I didn't have the option of the baby's chin technique, so I'm just taking a best guess at what I would have done if that was an option.
PPS I never tried ice, so I can't advise on that, but if I was still pumping and had a lump, I'd give it a try!