Hello Bilal,

All I recommend is to make sure you practice each variety as much as you can. I had to reset my English when I moved to the States to turn it a little more informal (I prefer to say everyday-ish). Now back to Tunisia and teaching English, I have found myself in the obligation to reset it again into a more academic English (at the levels of pronunciation and style especially).

Nothing makes a language skill better than practice (I am sure you know that too). I do a couple of languages so I speak out of experience. That said, it's totally fine to learn both at the same time.

Good Luck!

I think that a person can study ammiyya and fus-ha at the same time.  I studied fus-ha at a university in the US and I learn dialect from my friends.  I continually to study both fus-ha and ammiya.  I am able to easily memorize and retain both.  I might recommend using separate notebooks for fus-ha and ammiya even though I think many words and phrases overlap.  Since I have friends from many different areas I sometimes colorcode my notes: Egyptian ammiya in one color, Gulf ammiya in another color, etc.  Well, I wish you the best with your studies.  God bless. 

It's a good method to study Fusha and some arabic dialect at the same time if you're going to travel to a definite arabic country.

You learn Fusha as a language for speaking.

and you learn a dialect asa a language for listening.

Try to realize this idea :)

I think you can study Fus'ha and Egyptian dialect in the same time , but try to focus on Fus'ha. I think Egyptian Ammiyah is easy to be learned beside Fus'ha.

If it is up to me then I will study Fusha first.