I would go ahead and apply. Based on all the health problems you named, you would likely be approved, though it may not be on the first try. It is common to turn applicants down at first, then you can get a lawyer and appeal it (or just appeal it on your own.) You can take it all the way to a higher court if you have to, but I don't think you will have a hard time, especially since your doctor said to apply. Most of Social Security's decision is based on medical records and doctors' statements, so if you have a doctor backing you it will help a lot.
Good luck!