The Applications folder will not be in your own user folder (the house icon!) - although if you have added some apps, then applications will also be in your own user folder, if that's where you want them to be placed, and, if course, you can always add a folder to your own user folder with the name "Applications" if that's what you want to do. You do need to remember that Applications folder in your own user folder is NOT the Applications folder that your system uses for applications. Things can get quite confusing for you, if you put apps in your user folder that are more correctly placed in the systems Applications folder.
Most applications should usually be in the main /Applications folder, however.
One method to discover which is really the Applications folder on your hard drive (and not something on a completely different computer or external hard drive, for example), would be to go to your Finder (just click anywhere on the desktop) so you see Finder in the menu next to the Apple. Then click on the Go menu, and choose Applications from that Go menu.
And, then you will see the actual Applications folder that your system expects to use by default.
I'm thinking that you have just become confused about where your actual Applications folder is found.
You can make sure that the correct Applications folder is listed in the sidebar, by going to your Finder preferences, then click on the Sidebar tab. Make sure that Applications is checked, under Favorites. In fact, if you have a sidebar visible while the Finder Preferences is open, you can UNselect Applications, then re-select to watch the Applications disappear, then reappear each time you toggle that checkbox for Applications.
That will help you understand which is the correct Applications folder, because that will be the one listed in the Sidebar. I would suggest removing others, if they appear there. I would recommend that you change the name of an Applications folder, if you have made one inside your own user folder, to some other name. For example, instead of Applications, you could rename that to My Applications. I don't think the ML system will allow you to change the name of the system's Applications folder, so that will be your clue that really is your system's Applications folder.... Hopefully, that will help sort things out.