Q: upgraded my iPhone 6 to iOS 9.3.3 and now I'm starting to have issues

clean the device

Cleaning your Apple products - Apple Support

if problems persist you may wish to reset the device

Reset your iOS device to factory settings - Apple Support

it is advised you backup your data before doing this, otherwise you will lose it.

How to back up your iPhone, iPad, and iPod touch - Apple Support

jfonzo_77 wrote:

Will Apple Store help fix or replace my phone even though I do not have warranty? I have even Reset all settings on my phone but did not work.

Yes they will replace it but likely for a fee. See US prices below:

iPhone Repair - Official Apple Support

Have your tried a System Restore?

First backup your device using iTunes. Also import your photos to your computer and copy all important data. Try restoring from backup first and testing it. If it does not help, you may have to restore as New and reconfigure from scratch as the backup could be corrupted. For this reason it is important to have your photos and data saved separately from the backup. Here are the steps for a Restore:

https://support.apple.com/en-us/HT201252