There are several ways.
The first I'll suggest is select and copy these bits of the background that you previously missed into a third layer. Optionally merge that down into the previous layer you created.
Another way is to use the Clone Stamp Tool to copy from one layer to another.
There are others but you should investigate these two, anyway.
Instead of your workflow, think about this one instead.
You have an Image, with the Background Layer. You want to add material (pixels) from another Image to that. Select that additional material, and Copy it to the Clipboard. Then, paste it into the original Image, with extra pixels around that image. Add a Layer Mask around it, hiding the pixels, that you do not wish to see. Done.
It is so much easier to keep all the layers seperate when possible. It makes it much easier to edit later on. There is nothing stopping you from creating a new top layer that consist of all the other layers combined into one if you need to apply filters, etc. just use ctrl-alt-shift-e. Yeah its a whole lot of keys to hold at once, but it can be worth it.
Also as mentioned before you can merge all the layers into one , but should be done after your file is saved, then treat the file as a copy once the layers are merged. Then if you need to save, use save as instead and give it a new name. That way you can go back to your layers to edit if needed. As you can see ctrl-alt-shift-e is a better choice, since you only need the one file.