A ruptured disc is sometimes referred to as a slipped disc, prolapsed and herniated disc.
Because the disc is protruding this is putting pressure and aggravating the surround nerves and the muscles also go into spasm and that is why you feel the terrible pain.
Your doctor should sign you off work, prescribe you with diazepam or something similar, this relaxes the acute muscle spasms that are making it very painful for you to move. The doctor can also give you a pain relief injection and prescribe much stronger pain relief medication and an anti-inflammatory if you are able to take this. If you do get prescribed with Ibuprofen for example, make sure that you take this with or after food because it can cause stomach problems. Some doctors also prescribe Omeprazole to help protect the stomach.
When you are experiencing the acute pain (severe), you should be resting, but still moving about slowly. The doctor should give you advice on the type of gentle exercises to do so as you do not stiffen up completely.
The disc should settle down if you follow the advice from your doctor, take the prescribed medications as directed and take things easy.
I know it is difficult with you having a 4 month old baby, but whilst you are in the acute phase, it would be wise not to lift, push, pull or carry anything.
In the event that the disc does not settle, the doctor may refer you the specialist. You may also find it helpful if you can get someone to gently massage the muscles near the ruptured disc to loosen up the tight muscles. I used a massage oil that contains arnica on my husband when he slipped his disc and he found it did help him.
Be aware that even when the symptoms settle down, you are going to have to look after your back to avoid any more damage and further episodes of acute symptoms. Your back will have a weakness, so be careful.
Wishing you a speedy recovery.