Thank you for asking your query.
I have gone through the details you provided. Yes the colour of your stool - black/red can be due to the gastritis especially if associated with a bleed.
Black colour in the stool (typically black loose stools) is called melena. This happens when there is some bleeding in the upper stomach. This blood reaches the lower part of your colon, after some time and during this period some chemical reaction will occur causing the blood to be black. This appears as black stools. Red colour more or less implicates a bleed in the lower intestine.
But this doesn't mean you are having active bleeding. There are other conditions like certain food, infections etc. that can cause stool discoloration. Since you have been diagnosed with gastritis there is a possibility that it's causing the colouration.
It's good to know that your blood work and other tests are normal. You may continue to the drugs and syrup. If still the symptoms are persisting you will need to visit your Doctor again. You may need further tests to find out any occult bleeding.
It's also wise to test the Hb Haemoglobin levels occasionally.
Hope this helps.
Thank you for asking your query.