Can mold and a build up of dust in a 10 year old carpet cause chronic gastritis and heartburn?

Not likely. Mold may cause respiratory or skin symptoms but usually does not cause gastritis or heartburn. For info on gastritis: https://www.mayoclinic.org/diseases-conditions/gastritis/symptoms-causes/syc-20355807

It is important to remove dust and mold from the carpet or to change the flooring to a hard surface which is easier to clean. Watch for signs of wheezing,cough and itching.