Will Airplane Mode prevent data usage?

I recently bought a new phone, the Samsung Galaxy S4 and replaced it with my old 2011 Samsung Windows phone. When I had the Windows phone I never went over on my data. Then 2 days ago I bought the S4 and I've gone over twice in less than 24 hours… How? It makes no sense so I called AT&T and told them what was happening, (and by the way my wife had this same problem when she bought her Iphone 4s), They recommended no solution except for stuff I've already heard and they refused to lower my bill for data I didn't use. It's rather frustrating, the second I got my phone I turned mobile data off and made sure that apps couldn't run in the background without Wi-Fi connection. I fear I will go over again, so if I put it in airplane mode can that prevent Data usage? And if not what will?

It will, but it will sacrifice all other wireless communications. ( wi-fi, phone etc.)
Some things you can check is if you have data roaming on (this eats you're credit alive) and GPS as well. GPS uses quite a lot of data. Try that.

If you put your phone into Airplane mode nothing will come through. Double check that you have gone into settings and made sure that "mobile data" is switched off. If so, you should not be using any data over your network.

Airplane mode dare I use the term so early in the day
" OK strong language be warned"

Make the S4 an IPOD. Well more a MP3 & MP4 player NOTHING comes through No calls NO texts

The S4 (apologies S4 I know and I won't use the term again it was WRONG) has an inbuilt data Monitor

Also Google Play has FREE data monitors which you can install on your phone, these will tell you APP by APP where or what you are doing and are fairly accurate.

I have 3 Data monitors, the installed and 2 other which give me All the information I require.https://play.google.com/store/search?q=data%20monitors&c=apps

A few don'ts, DO NOT UPDATE APPS on 3G or 4G as that comes out of your allowance use Wi-Fi
Emails and constant syncing again use your allowance you may be reloading email you have already read

You have NOT stated what you allowance is say eg 1GB per month is ONLY 34Mb per day which can go fast if view Youtube

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Almost forgot as I don't use it, you can set the Data Monitors to disable the WWW once it hits XMb per day per month and warn you prior at Ymb

You have to bear in mind that At&T figures are the figure that will prevail as monitoring is not an exact science when it comes to measuring