Clearing Notification center

HI, I am using a iPhone 4s with current ios, ios 9, and its been an ongoing problem actually. i have notifications go to my notification center. UPS, xbox smartglass, amazon, and a few others. When i swipe down and clear it, hit x, than clear. It takes like a minute for it to complete and as it clears that days notifications it seems to kind of blur older notifications being "wiped" as well. I can glimpse see some dates some being....realllllly old. Like 2,3 even 4 months ago. And my take on it is that my phone or the phone on general doesnt delete thrm fully. But rather just makes thr notifications hidden. Now this may be why my iphone is uber slow at everything, thats its just carrying around super old data constantly. Is there a way to wipe it clean? Or is going full wipe of my phone and readding things manually my key to that.