Armstrong Ultra SX90 Furnace problem
Even though HVAC is not my specialty (electrical is), I have worked on HVAC controls for Energy Management Systems. As far as I know all heat units have a cool down cycle so when the heat turns off the fan continues to run to softly cool down the unit. This could either be a timing relay or thermo sensor which tells the fan it can shut down. 

So that's where I would look. My thinking is that this devices is bad and faulted to a normally on position where the fan is running all the time. As a DIYer I don't think it wise to get into HVAC controls unless you had some experience and are good at following schematics and finding part numbers for replacement. I am suggesting a qualified HVAC mechanic should be doing this repair. 

Good luck and stay safe.