The symptoms you are describing—specifically a small, soft, reddish tissue that protrudes during straining and retracts on its own—are not considered a normal finding, but they are very common and highly treatable.
Your suspicion is quite accurate. This presentation is a classic sign of Grade II internal hemorrhoids or a localized rectal mucosal prolapse. Grade II internal hemorrhoids characteristically prolapse (protrude) during a bowel movement or straining but reduce (go back inside) spontaneously afterward.
While stress can certainly exacerbate gastrointestinal motility issues and lead to altered bowel habits or straining, it does not directly cause physical tissue protrusion. The medications you were prescribed (a probiotic and a gut/stress modulator) may help manage bowel consistency and stress, but they do not directly treat the physical structural protrusion.
Next Steps
Seek a Second Opinion: Because you have a clear, reproducible physical finding that was not fully addressed, it is highly reasonable to consult a different general surgeon or, ideally, a colorectal surgeon (proctologist) for a dedicated evaluation, such as an anoscopy or proctoscopy.
Avoid Straining: Try to avoid prolonged sitting on the toilet or forcing bowel movements, as this worsens tissue protrusion and hemorrhoidal swelling.
Optimize Stool Consistency: Ensure your diet is high in fiber and drink plenty of water to keep stools soft and easy to pass, minimizing the need to strain.
Health Tips
While it is reassuring that you currently have no bleeding, you should seek prompt medical attention if you experience any "red flag" symptoms, such as:
The protruding tissue becomes trapped outside the anus and cannot be pushed back in (incarcerated or strangulated hemorrhoid).
Sudden, severe anal pain.
Significant or persistent rectal bleeding (bright red blood in the toilet or on the wipe).