Hi there, here are my corrections to your writing.  I hope this helps, let me know if you have any questions about them!

A particularly officious custom officer suspects(must be past tense because it is a story) suspected that the ('the' writer if we already know who the writer is)writer was trying to smuggle something through customs(we don't really use the word 'smuggler' as a noun anymore because it sounds quite old-fashioned.  We prefer to use the verb 'smuggle' in some form) to be a smuggler unless he could and wanted to unlock his suitcasea to check it.for checking. With While ('while' is used to talk about something that happened during another continuing action)carefully searching the case, the ('the' officer because it is a noun and it needs something before it 'a'/'the'/'his'/'her' etc. 'The' is the one we need because we know who the officer is)officer spotted a tiny bottle, and with delight a face brimming with delight and he sarcastically asked the writer is that a if it was a bottle of perfume.  (always a space after a full-stop)Although The writer explained that is this was his hair gel which he had made by himself, but the officer didn't believe that,  and so he tried to smell the bottle with writer's permission.  Finally, (always a space after a comma)he got the truth answer realized that the writer was telling the truth, and he let the writer him pass through.