In my practise, we deal with back and shoulder injuries all the time. It doesn’t seem that you had any particular accident at work but the conditions that you describe are certainly very hard and it is very unfortunate that you were so unlucky.
Generally, if you had an injury at work, the first thing you do is take photographs of the accident location, tools and machinery you used. If you picked up a heavy box and suddenly felt pain in your back, take a picture of the box and note how much it weighed. This is can be crucial to your case. You must also tell your employer that you have had an injury or your back is sore. Not many people do that because they are afraid to lose their jobs and indeed the employer can require you to bring a certificate from the doctor that you are fit for work. What we have experienced, people work without complaining up until they cannot get out of bed one day and as a result of working with sore backs they have terrible back injuries that dramatically affect their lives for the rest of their lives.
In your case, the time will be calculated from the time you first realised that you injury is related to your work and this is usually when you go to the doctor. We deal with these type of cases all the time in our practise and I would certainly recommend going to a solicitor, even though this is not the most straightforward case.
It sounds like your employer has failed to meet the standards required by law, and you may well be entitled to compensation for any injury suffered by you as a result along with all out of pocket expenses to include medical expenses, hospital charges and loss of earnings.
Some of the accidents at work which we have handled over the past number of years include manual handling, injuries caused by lifting and carrying heavy items. A lot of our clients work in warehouses and distributions centres where the demands made of them by their employers are very often excessive and often result in serious back, arm and shoulder injuries.