Over the counter stuff from one country may be prohibited in Dubai.

Having said that, I carry lots of over-the-counter medicines from the UK to Dubai to cover all sorts of travel ailments and have never had an issue at Dubai customs.

Personally I wouldn't bring food in. You can eat very well in Dubai with great quality food at very cheap prices.

In my years of travelling to Dubai I've found that you don't need to take much stuff with you other than clothes. It's a very developed place with modern infrastructure and everything is available there. Literally, everything!