Can back pain be fixed without chiropractors as long as you exercise your back?Your question assumes 2 things.
First assumption is your back is "broken" and needs to be "fixed".
First thing you need to do is find out what is wrong with your back. Get an examination and get a diagnosis.
Look up the incidence and causes of low back pain and you will find some interesting facts.
1. The incidence of low back pain (generally) increases as we got older.
2. Many problems can cause low back pain, from serious and life threatening to benign and self resolving.
3. Low back pain is one of the most common ailments globally.
Second assumption is exercise is somehow a replacement for chiropractic.
Exercise is not a replacement for chiropractic care, nor is exercise a panacea for all types of low back pain.
Back pain should not be ignored or treated in a cavalier manner.
In my own experience proper exercises coupled with proper chiropractic care have done wonders for people.
If you have an aversion to chiropractic care do yourself a favor and go speak with a few of them in your area. Most would be happy to answer your questions. I would caution against seeking a diagnosis on the Internet.