Generally, it is OK to simply blow your nose in Japan.
Japanese people don't blow their nose because they (especially most men) usually don't carry tissues, and because they can't throw away the tissues readily since there is practically no trash bin available in public.
But I just googled it and got pretty surprised to see that some people consider it unpleasant to blow their nose in front of others. It is ridiculous, as keep making an obnoxious noise by constantly sniffling is definitely more unpleasant!
But it seems the divided opinion. I would rather like to see the poll by region, gender, and generation...
Your friend got the hilarity because of the "trumpet-like" sound; hilarity is never close to hostility, so don't mind it.
If you care about these naggers, it might be wise to go to a bathroom and blow your nose there. But I believe it goes too far and you don't need to. I also frequently see people blow their nose, especially middle-aged and elderly men but no one around them minds it!
(But for some reasons I have rarely seen women do, and in fact the google search got me to know some naysayers dislike the blowing nose only if they are women. Ridiculous...)
And some people seem to hate only when they blow their nose while eating, so you shall refrain at the dining if you care about these people.
There seems to be no poll on the web, but one website asked its readers which of sniffling and blowing is more unpleasant. Note that this website is strictly designed for wives, and over 80% readers are between 30 to 49, I guess.
- sniffling is more unpleasant: 41 votes
- blowing is more unpleasant: 7 votes