Are Umrah and Tawaf valid after doubting that something came out of the anus, and it was later found to be worms, while being uncertain of the Shari'ah ruling at that time?

If you doubt the time of the worms' emergence, consider your circumambulation (tawaf (definition)) valid, because an incident is attributed to the nearest time.

However, if you are certain that the tawaf occurred after the worms' emergence, then your 'Umrah (definition) is invalid according to the majority of scholars due to the condition of ritual purity for tawaf. You must cease all actions forbidden during ihram (definition), then return to Makkah to perform a valid tawaf, followed by Sa'y and taqsir (shortening the hair). For any destructive forbidden acts you committed (such as cutting hair), a single fidyah (definition) is required for each type; as for acts of comfort (like perfume), there is no penalty due to ignorance. If sexual intercourse occurred due to ignorance, the 'Umrah is not invalidated.

If you are unable to return to Makkah, you are considered like one who is prevented (muhsar), and you can exit ihram by sacrificing an animal (a sheep) or by fasting for ten days if you are unable to sacrifice.

It is permissible to adopt the view of the Hanafis and one narration from the Hanbalis, which does not stipulate ritual purity for tawaf. In this case, your 'Umrah is valid, and you owe a fidyah (a sheep) for the emergence of the worms.