Another sufferer here.
My sciatic pain was so bad that I would have jumped off a cliff had I not been operated on. I only lasted three weeks with the pain before surgery and I will never forget the horror of the pain, so I do understand how you feel.
In my case, surgery was the only option but if the disc has herniated higher up it is possible to wait it out and the disc may.. recover, so you would not need surgery. You obviously need good advice from a neuro-surgeon after having MRI/CT/x-rays etc. Only then will you know how damaged your spine is.
Until you can see anyone (please don't leave it) regular painkillers may help and gentle stretching exercises, if you can tolerate them could also be beneficial. There are many online but with all of them, very very gently does it - you are trying not to irritate the nerves.
I wish I could give you brighter news: to sum up, see a GP and ask for a referral to either NHS/private neuro surgeon as soon as you can; take regular painkillers (don't take more than the recommended dose); do very very gentle stretching exercises.
It goes without saying that you should not carry anything remotely heavy - even a kettle or pain of water can be too much.
I hope you are better very soon - you have my sympathy.