A few things I don't understand: You say that you went to the DMV and they "supposedly" did an address change at least twice (each time you registered a new car). Did they give you a new license or did they give you a sticker to put on the back?
Also, you say your license was suspended because you didn't take a driver retraining course. Why did you have to take this course? I am asking because if there was a prior offense to the cell phone offense, you would/should have learned about a suspension then. For example, if you had a DUI, you would definitely have learned that. So it doesn't add-up that you got suspended without knowing.
Personally I don't think you have a good cause or cause for an attorney, but that's up to you. Unless you can prove a license address change at the DMV, your prior offenses which resulted in a suspension will not look good infront of a judge in the first place. I suggest you start at the DMV and follow their instructions to the T and get clear with them. On your court date you will get a change to explain your side and what you have done to resolve the issue. If they decide to suspend your license for an additional 30 days, I suggest you just take the suspension if you can find a way to still get to work.
The reasoning for not bothering with a lawyer is that it will be a cost to you and that you will not likely get any kind of compensation back. So the lawyer is only there if they can save you money. Do a cost analysis of what it will cost you to take a taxi or public transport every day for 30 days to/from work (plus additional trips to the supermarket) vs the cost of the lawyer. Assuming a transportation budget of $45/day, that's $1350 for 30 days. If your lawyer can fix the problem for less than that, then sure, why not. But frankly, I think your prior rap sheet will factor in and you are just as likely to lose the case. When it comes to the DMV, expect to get screwed. So it's a gamble. You could be paying the cost of a lawyer + the cost of public transport.
If it was me, unless I had a very far commute, I'd try to fight the 30 days suspension in court myself and hope for the best. If that failed, I'd just take my medicine and deal with the 30 days suspension and be done with it.