things I"ve used are:
steaming DD in the shower three times a day
(ie standing in the bathroom as I steam it right up, and then stay in there for a while - helps to keep it loose and runny!)
when i"m nursing, i spray my milk up her nostrils to help clean it out
Suction to get it out.....once I even sucked and spat - though not my favourite method!!!!
Ate vitamin c and roasted garlic myself to help her fight it - and I understand that rubbing flax seed oil on their belly helps to boost their immune system (ie it is absorbed into their system at a time when they are not eating) but I don't know if you want to try that with a one month old (maybe ask a health care person of sorts?) We did it with DD at 2 months, and it was fine.
Best of luck! We're finally recovering from an illness that older DD got, then passed on to younger DD and now I realize that illnesses are going to go on for a longer period of time now that we have two!!!