Is it normal my feet always smell at work?

I'm sorry to say that if your feet smell and your nose runs, you are built upside down.

You are normal. Just think of it this way. Your feet smell because you're a hard worker. There's nothing wrong with that.

I don't see the issue. Smelly feet are the sign of a good worker. ;)

Put baby powder in your shoes every time you wear them. It will soak up the sweat and after a couple weeks your shoes wont smell anymore. This worked wonders in my teens

Get some Odor Eaters inserts.
http://www.odor-eaters.com/

It's mainly the socks. Get a different fabric. By now, however, you may also need a new pair of shoes.

If it's that big of a problem wear the non-smelly stuff at work.

Calcium undecylenate

Keep your shoes on at work.