Brief Answer:
Please get a stool test and complete blood count done

Detailed Answer:
Hello

Thanks for asking on this platform

Loose stool if persists for more than 14 days should be thoroughly evaluated.
As the loose stool was associated with vomiting there is high possibility of associated infection.
Here infective causes should be ruled out by complete blood count and stool routine examination.
Other causes of prolonged diarrhea which causes poor absorption or allergic causes like celiac disease should also be searched if infective causes have been ruled out.Presence of sac like thing in stool can be mucus and it can be there in parasitic infection.
Sometimes it may take longer duration for stool pattern to get normal after an infection.
Loss of absorptive area due to acute infection may be the reason.Here avoiding sugar/sorbitol containing items like juices/fruit syrup,milk, wheat helps in early recovery.
Giving probiotic and zinc supplementation also helps.
Give plenty of fluid to avoid dehydration.
You have mentioned that celiac disease and parasitic infestation has been considered.I request you to attach the report if it is done so that I better able to help you out.

I hope this helps.
Please let me know if you have any more doubt.
Regards

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Brief Answer:
I appreciate your observation

Detailed Answer:
Thanks for follow up

I really appreciate your observation and there is high possibility that the sac you have noticed is unabsorbed part of orange.
Teething usually does not causes prolonged diarrhea.
Please consult a pediatrician for evaluation and management accordingly.

Wishing for your baby's speedy recovery.
Regards

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