Max of 5ml refers to one site, so if you need more, put it in one syringe but only put part in, then move the needle for the rest.
Antibiotic resistance develops quicker when animals are underdosed, so always weigh or estimate on the larger side. Alamycin is a safe drug so 6/7ml will do fine in two bits.
Keep milking her out if you can, as getting the infected stuff out will speed up her recovery.
The lambs should be fine to leave with her, if she's uncomfortable she won't let them suck, and if its bad milk they wont like it. Just make sure to top up if they're hungry.
An anti-inflammatory pain relief injection is often overlooked but can help with discomfort and healing.
All the best
Suzanne