The JPGs on my Nikon D7100 (24Mp) are around 20Mb per photo, so your situation is not unusual. Lucky you are not using uncompressed RAW or they would be even larger.
And I am told that with the Nikon D800 (36 Megapixel full frame), RAW file sizes can approach 100Mb per photo!
If you are shooting photos for the web, you should either reduce the resolution and size of the photos in your camera, or use a post-processing software to do so.
With high performance cameras, you only need maximum resolution if you are doing fine portraiture, landscapes, etc. where you want to hang a large photo on the wall. Otherwise, for everyday use, you can lower the resolution.
Especially for the web, you don't need a high resolution.
Most DSLRs have a Small, Medium, and Large size setting along with a Basic, Normal, Fine resolution setting. Large/Fine creates the highest quality with the largest file sizes, while Small/Basic creates the smallest.
You should be using Small/Basic for the web (which is still a high quality photo).
But some people prefer to use Large/Fine for everything which gives the best photos - then make a copy and reduce the size/resolution in post-processing software. That way, they have one copy for the web, and the original for making a wall photo if they so desire.