Hi Lauraloola
Sorry this has taken so long, just spotted your post on my thread as my youngest is unwell at the moment...
I probably don't need to start about how everyone is diffferent etc so will just start with you!
To get an urgent physio assessment (as opposed to 6 month wait) you need to tell your GP about your CURRENT episode ie just few days since onset, emphasise problems caring for your little baby, and once you have the referral, call the physio department that you were referred to and keep calling and again emphasise your acute problems. Otherwise it will be seen as a chronic problem and treated as such.
In the meanwhile I would also try anti-inflammatories (assuming there is no reason why you cannot).
As Morningpaper so wisely advised, you need to keep moving as much as you possibly can. Your back is NOT a 'no pain, no gain' situation, and you should not aggravate it by movement, but exercise like going for walks or possibly swimming would be very good especially at this early stage.
Physio assessment (underwear only )will include many things - posture, muscle spasm, movement quality and range, spinal movements by pressing on joints of the spine to check the movement at each level, neurological involvement - to see to what extent the nervous system is affected, dynamic movements eg how you lift, turn in bed, carry your baby. It should not be painful at all.
Treatment should include manual therapy - targeted at the muscles and joints affected the first few sessions, and the most important bit (MORNINGPAPER!!!!) is the ongoing management which largely depends on you doing your exercises, but not exclusively. Of course you could end up with very experienced physio or the opposite, but in general the exercises prescribed can make an enormous difference in recurrence rate. You can be relatively sure that this episode will get 'fixed' soon, but maintenance will be important for you for a couple of years to allow healing to take place. I know it takes a large commitment to keep doing boring Pilates-style core strengthening exercises when you are busy with a small child, but it is really worth it in the long run.
Good luck! Any more info required I am happy to advise, but am in USA at the moment, so advance apologies for delays.