Dragging photos

You can drag and drop an image on a Mac onto the PS icon in the dock. This does NOT work on a PC. You can drag and drop images from the desktop directly into an open Photoshop document - I do this all the time and there is absolutely no propblem doing it this way. You can also drag and drop an image into an open PS doc from Adobe Bridge. This is my preferred method. You can also simply place a second file into your PS image from the file menu. 

Also - if you are trying to combine 2 images and simply need them both opened in one document as layers, you can use Bridge. In Bridge, go to the tools drop down menu, choose Photoshop and choose Load files into Photoshop layers...

Regardless of whether it "should" work or not, dragging and dropping is simply bad practice that should not be encouraged. Very often you don't open the original file this way, but a thumbnail or low quality proxy image. Try to drag from Firefox, for instance, and you get a bitmap .bmp with color profile stripped. That's just one example I personally know of, there are plenty others (and some of them show up here in the forums).

Save the file properly, then open it in Photoshop.

Are you talking about Photoshop Express https://helpx.adobe.com/photoshop/using/photoshop-express-help.html#Getstarted? 

Please upload screenshot of Photoshop on whatever device you are using it. I know there was Photoshop Express few years back but I am not sure it is still available as online application unless you are using it on Android or iPhone.

"school is providing me with an online version of photoshop"

Which exactly online version of Photoshop? Can you provide us with more info about application that you are using?