Yes milk out as much as you can (but not empty it, just ease out), and she will need twin lamb drench plus Calcium injection, as she probably has mastitis AND milk fever.
There is also a product called EWE-GO, which is a drench and has both glucose (for energy) and Calcium (for milk fever). Probably from your vet. I have not used it but it comes recommended from another goatkeeper. Also she will need an antibiotic for her mastitis - so I think I would call out the vet. Vet can administer Calcium directly into her vein, and will also have twin lamb drench. She will need to same dose as a sheep for both. Give her as many treats as she will eat, but no high-protein goat mix - so shreds, hay and a few oats should be fine. PLus loads of veg/fruit.
The limping is also a sign of mastitis, as she is in pain on that side.
Do her kkids have had colostrum and does she let them suckle? If not - give it to them in a bottle asap...
She will need lots of TLC for the next few days