especially since I have external bags attached to my urinary and intestinal outlets through which I relieve myself; they are fixed to my body, and something may come out of them without my sensing or noticing it while I am praying. Given this situation, is my prayer valid or not?

Answer: We ask Allah to grant you recovery and well-being from what has afflicted you. As for the ruling on your prayer when something exits from either passage without your awareness and you are unable to restrain it, your prayer is valid. Allah the Exalted says, “So fear Allah as much as you are able” (64:16), and He says, “Allah does not burden a soul beyond its capacity” (2:286). The Prophet (peace and blessings be upon him) likewise said, “When I command you to do something, do of it whatever you are able.” This is the limit of your capability.

However, you should not perform minor ablution except when you are about to pray after the time has begun. Make ablution, pray immediately, and complete your prayer even if something comes out during it, for you are unable to do any more than that. Allah knows best.
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The Prayer Is to Be Offered Within Its Time According to One’s Ability

Question: A patient sometimes misses the dawn prayer because at times he cannot face the qiblah and cannot turn toward it, and because no one is available to bring him water and help him perform minor ablution. May he perform the prayer before its time or delay it until after its time?

Answer: It is not permissible to offer the dawn prayer before its time, nor is it permissible to delay it beyond its time.