Of course, you can ask for an emergency order whether you have valid or not. However, based upon the facts, it does not appear that you have any grounds that rises to the importance of having such an order granted.
It might work to your advantage to obtain a lawyer to advise you on the matter. If you cannot afford one for the entire matter, you should consider taking the time to visit an attorney's office for an initial consultation. Discuss all issues in your case, including the grounds (if any) for an emergency order.
I strongly encourage you to contact an attorney. You can not file a counterclaim to a contempt because a contempt is not a complaint pursuant to the Civil Practice Act. See Carden v. Carden, 266 Ga.App. 149 (2004).
I would encourage you to have him served on the modification when you go to the court for the contempt. If you have not already done so, you can file a motion for the appointment of a special process server and have him served using a private process server instead of the sheriff. Provided you have some information regarding his whereabouts -- where he works, where he goes to the gym, etc.
This post does not create an attorney client relationship. This attorney is only licensed in Georgia.