You made hardly any mistakes! Well done! Your writing is really good.

Dear Sir or Madam, 

I am writing to inform you of an unsatisfactory experience / I am writing regarding an unsatisfactory experience to which I was subjected upon my arrival at your hotel last week.

My family and I were staying in your hotel from the 21st to the 24th of November. We made a booking for two double rooms three weeks in advance using your online reservation system. When I arrived at the hotel [you have already stated "your hotel" once, so the reader now knows whose hotel it is. From now on, you can just say "the hotel"] and asked the receptionist for the keys to our rooms, I was surprised to hear the receptionist inform me that no reservation in my name appeared to be in your system. [If you say "no reservation was there" that means it is a fact that it did not exist. Clearly, you dispute this. You do not agree! You remember making the reservation. Therefore, I think that it is best to say that no reservation appeared to be there. ]

After an eight-hour tiring flight from Tehran to Kuala Lumpur, being greeted with the claim that our hotel reservation did not exist was not something that we had expected. Once your receptionist realized how frustrated we were, she asked for the payment receipt from / for our reservation, which I fortunately had it in my pocket. [Your word order isn't wrong. "I fortunately had" and "fortunately I had" would both be correct. I just prefer writing it that way. Do not say "it" if you have already said "which". ] Upon being shown the receipt, she managed to find us a room, but we had to be given a quad room since all the double rooms had already been booked.

In order to prevent such problems from happening again in the future, I would like to respectfully suggest [using the adverb "respectfully" when making written requests makes the request sound more formal and polite] that you audit your reservation system to find out why it is not storing some reservations. Were it not for your sympathetic and accommodating / resourceful receptionist, ["attentive" is a very good word. Well done! I have suggested some synonyms that might be even more suited to this particular context, but "attentive" is already a great word to use] we [you were not the ones who solved the problem. Therefore, I think this part should be written in the passive voice] this problem might not have been resolved in a satisfactory manner and it could have ended differently.

Yours faithfully,
Mr Adib Yz

I encountered a problem when I was staying in a hotel in Malaysia.

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I think the writing is brilliant and as you can see, only minor corrections had to be made. 

Good luck!