Hello! I would suggest trimming your relaxed ends. I know you don't want to do the BC but if you hold on to the damaged ends, your hair will constantly break. I didn't do the BC because I didn't want really short hair so I understand where you are coming from. I did, however, cut a few inches off at first and then periodically I would go to the salon and have them trim a little.
As far as your hair growing slowly, there is not much you can do in the way of making it grow faster. What you can do is take very good care of it so that you can retain the hair that does grow. So moisturizing the ends of your hair well is key in my opinion.
You don't have to spend a lot on hair products. I use shampoos and conditioners that you find in the local pharmacy or grocery store.
I hope this helps!