We are at an era where carrying a sword was normal, right?
For a noble or soldier of fortune, yes. Or a huntsman of some description, though they would usually carry an axe and maybe a shortbow or javelins (because hunting is better done at range). Most people don't wander around armed with anything more than a simple iron knife (the peasant's tool of choice for all manner of tasks).
Swords, it is worth noting, are something of a nobleman's weapon. The common soldier doesn't get trained in the use of a sword because swords are actually very difficult weapons to use - without extensive training you are as likely to cut your own limbs off as anyone else's. Maces or spears are more commonly used by soldiers (spear fighting especially for formation work, with maces having an edge in close combat), but the tool of choice for many soldiers is a simple compromise - the axe. Axes are probably the most common weapon available in this era, not least because with the exception of the most specialised battleaxes they also work quite well as tools for a variety of tasks a soldier might need to engage in (e.g. chopping wood, clearing brush, cutting ropes etc).
Additionally (although this varies by region) many places actively prohibit commoners from carrying weapons openly, and some places prohibit them from owning weapons outright. This is most often to get around people using deadly force and rising up against their masters, or simply from causing chaos in the streets. The idea that all men have the right to bear arms was a result of the revolutionary period (at least in Europe) - most governments have had the good sense to deliberately restrict their populace from wandering around with weapons.
But no, swords aren't obsolete. If someone saw you with one then depending on how you were dressed they might think you were a noble, an experienced soldier or someone who's gone and stolen a sword.