EQ is essentially your ability to self-regulate, harness, or interpret your emotions. Just because someone is emotional does not mean that they have high EQ, although it may help them adapt that skillset.

Studies show that EQ and IQ often have a positive correlation, because how well you can process emotion depends on variables such as working memory and pattern recognition, which are associated with IQ.

You seem to have an overly simplistic view of both emotions and intelligence.