Do you have the Limit File Size To: box checked? Export (File Settings)
A 3 megabyte export may be the right size, but you cannot tell if it is full resolution or not by looking at the megabytes.
If your original image was (for example) 6000x4000 pixels, and the export is 6000x4000 pixels, then you have a full-resolution export.
So you need to examine the pixels in your original image and the pixels in your exported photo, and if they match, you have a full-resolution export. And since you did not check resize to fit, I expect this is what you will get.