Dont worry about manual updating the firmware, Odin is a Samsung tool that is not supposed to be public, frankly, it is the easiest solution on the android world to flash a firmware.
When i upgraded my phone, i was aiming to change the CSC code, and i actually flashed the full wipe way, but i had the SIM in which kept the old CSC (my CSC and SIM location match anyway).
When you download the firmware, there will be 5 files, which you have to load 4 of them in Odin, the CSC_### will wipe everything, the HOME_CSC_### will not. All these files will update everything for you, newer to what you missed so far with the OTA's.
What i did resulted in what i did not aim, however, if you do what i did, it will lead you to have the CSC where you are currently, which will most probably give you the OTA's in the future. And you dont need OEM Unlock to flash official firmwares.
In summary:
1. Make sure you backup first as it will wipe everything. Also, for the sake of taking things normal, make sure you
dont have things like FRP/Secure Startup on (the ability to put a pin/password in order to boot), and also log out of your Google account.
2. Download firmware and flash BL, CP, AP and CSC respectively (ignore HOME_CSC), it's easy to know which file goes to which tab

.
3. Keep the SIM inside.
4. Have a look if CSC has changed.
You're good to go.