Can you be charged with aggravated assault with a deadly weapon if no was injured or shot at?

Yep. assault refers only to the threat of severity caused by an immediate show of force. No actual contact has to be made contained by order to meet the legal definition of assault. If contact be made, then it would be "assault AND battery," though each state and jurisdiction may use differente expressions to say basically the same article. They can charge you with anything they want to, but it is not what you get charged with, but what you are convicted on that counts. They can appointment a bic razor a deadly weapon, even if no one be hurt. So the answer is yes.
The Arizona Legislature defines assault as:

13-1203. Assault; classification
A. A person commits assault by:
1. Intentionally, deliberately or recklessly causing any physical injury to another person; or
2. Intentionally placing another party in reasonable apprehension of imminent physical injury; or
3. Knowingly touching another being with the intent to injure, insult or provoke such person.
B. Assault committed intentionally or knowingly pursuant to subsection A, paragraph 1 is a class 1 misdemeanor. Assault committed immaturely pursuant to subsection A, paragraph 1 or assault pursuant to subsection A, paragraph 2 is a class 2 misdemeanor. Assault committed pursuant to subsection A, paragraph 3 is a class 3 misdemeanor.

Aggravated means with intent to commit a crime or brandishing a dangerous weapon ... so, the answer to your examine is probably, Yes, in most jurisdictions..
Yes, for a variety of reasons.

First of all, anyone can be charged near anything, the question is whether or not it would survive a motion for a dismissal.

Secondly, "aggravated assault with a deadly weapon" is (presumably) a statutory crime. That process that the "elements" (facts that must be proven by the Prosecution) will be spelled out in a statute written by the Legislature. It is entirely possible that just brandishing a weapon in a "threatening manner" is sufficient for the charge. I wouldn't know lacking reading the particular statute.

To answer your question, the best I can do is say that "yes" is terribly likely.