If there is no 'update' listed in your "Settings" on the phone, then there is no update for that phone. Just because there are newer versions of Android doesn't mean that the phone you are using is made to handle them.
However, this likely would not cause the problem you mention. Sounds more like there is to much on the device. To many apps, files, etc., taking up space, as well as, any apps you continually run without clearing them out (facebook, browser, etc.) will use up your resources.
You may want to consider backing up your files and data (not apps as those you can't back up) and do a full "Hard Reset" of the phone. This would put the phone back to its original state (before you installed anything) and then you can redownload your apps and move the other stuff you saved back to the phone from where ever you saved it (just don't save to a SD card as that is not wise). The phone should work much better then.
Additionally, in the future, I would suggest closing apps rather than leaving them open in the background using up your resources. Also, you should restart (power off and back on) the phone often to clear resources.