Bioballs certainly do not build up ammonia. I think that was a type.
They also DO NOT build up nitrates per se - PEOPLE build up nitrates - from overfeeding, overstocking, improper maintenance, etc. Regardless of what you use as a filter media, you will have nitrate problems if you do not have enough nitrate export (water changes, macro algae, deep sand bed, etc.).
There are loads of systems that run just fine with bioballs. I do not recommend you make any major changes to your system right now until things are settled. And even then, I would not recommend removing bioballs until you feel really confident in your tank keeping skills. I would rather have a nitrate than an ammonia problem, and bioballs are EXCEEDINGLY effective at growing bacterial populations to quickly use ammonia.