Does Cel phone charger drains the battery

If you are charging the cell phone while driving, the phone’s charger is actually drawing less current than accessories such as the rear window defogger. Ergo–that charger is not a high current draw.

On the other hand, if you were in the habit of doing this while the car was parked, that would be a good way to kill a battery. Apparently, you were doing the charging while driving, so this practice should not have killed your battery.

How old was that battery?
If it was the original, it was WAY past its normal operating life.
Even if it was the second battery, it could well have been slowly dying, as many batteries do not last beyond 5 years.

Also a factor is how long that commute to work actually is. When engines are started and cars are driven only a short distance before shutting the engine off, the battery never gets fully recharged.

In order to get the most life out of your battery, you need to:

Drive long enough distances to keep it fully charged. If you typically do a lot of short-trip driving, then on weekends you need to take the car out on the highway for ~45 minutes in order to preserve the battery, as well as the engine and the exhaust system. If you can’t get out on the highway for at least 45 minutes each weekend, then you should invest in a trickle-charger for your battery.
Keep the top of the battery, as well as the terminal connections clean. Periodic cleaning with a solution of baking soda and water will neutralize corrosion (that blue-green residue on the terminals).
Make sure that the terminal connections are tight.
Make sure that you turn your lights off when parking the car.