Whoa! 20ppm nitrate!!! Dude, water change time!!! You don't want your nitrates to be much above 5-6ppm! For 35 gallons I would do a five gallon water change (with gravel vac) tomorrow, then monitor your ammonia/nitrites/nitrates and do water changes until you have your nitrates under control. Also, test your tap water for high nitrates. Sometimes depending upon where your water supply is the tap water may have high nitrates to begin with and this will not be healthy to add to your tank. If that is the case, you will need to consider going to RO water.
I can't tell you if your barbs will be okay or not. Only time will tell. Do not add any more fish to your tank for at least the next three weeks. Even if you do get your nitrates down, you must monitor to make sure they remain stable. Only once stablity has been achieved would you want to cautiously and slowly add a few more fish.
~~Colesea