macOS High Sierra is not supposed to show as an available "update." However, you can download the "Free Upgrade" by selecting the updates tab in Mac App Store and selecting the "Free Upgrade" button at the top of the window or by searching "High Sierra" in the search bar of Mac App Store.
While holding the Option key, select the battery icon in the Menubar. Your Mac will give you a readout of the condition of your battery. If it says the condition is "Normal" then continue with software troubleshooting. If anything other than normal, replace your battery either at Apple Retail or an AASP.
If more software troubleshooting is needed, check Activity Monitor > Energy to see which applications routinely use alot of energy. Reinstall applications as necessary if they're found the be energy hogs. If no specific apps are found to be the culprit, a restore of macOS is more likely to resolve the issue than an update.
To restore, hold Command-R during startup > Disk Utility > select Macintosh HD > Erase. Then quit Disk Utility > Install macOS > select "continue" and "agree" as necessary.