Hello Baham,
I am sorry to hear you are having troubles with your phone, the problem isn't your phone however it is your battery. The Note 3 drains the battery so quick that it ends up killing the overall life of the battery!
I would check eBay for an OEM part, don't go for the $4.99 one it should be around $25. This will ensure that the battery will last more then a week!
Hope this helps, Good luck!