Share your experience!
I can't seem to tap or press anything on my screen at all. In fact, it keeps going "haywire" and starts tapping and responding at completely different parts of the screen. All the physical buttons do work though. But the as soon as I turn on the screen/phone, it starts going haywire even if i don't touch it (the screen).
Now whenever I try to switch the phone on it gets really really (really) hot and I've to force shut down it.
Hi Sony-Isa, welcome to the community!
Ensure the phone is charged and backed up.
Back up your phone using PC Companion
1. Go to Support to install PC Companion on a Windows
computer.
2. When installed, start PC Companion on the computer.
3. Connect your phone to the computer using a USB cable.
4. Click Start under Backup & Restore.
5. Follow the on-screen instructions.
(Exactly what contents will be backed up may differ
depending on phone model.
You can view detailed information about this as you follow
the steps in the Backup & Restore wizard).
Back up your phone using Bridge for Mac
1. Launch Bridge For MAC.
2. Select "Back up your Xperia device".
3. Select the data you wish to back up from your device
(the windows can be expanded for more detail as below;
then select "Next".
4. The backup will now be in process, do not disconnect
the phone while this runs.
After doing the back up, power off your phone and disconnect it from the computer. Begin the steps below until you are prompted to re-connect the device.
Running the software repair on PC Companion:
1. Install and open PC Companion then select Support Zone.
2. Phone Software Update.
3. Start.
4. Repair Phone
5. Continue
6. Accept data removal
7. Next
8. Wait for prepare
9. Select Phone
10. Follow the connection steps
or running the software repair on Bridge for Mac:
1. Launch Bridge for MAC without the handset connected.
2. On the Main Window select "Xperia > Repair Xperia
Device".
3. Ensure the phone is charged and select "Ok" in the
following window.
4. Select Continue on the following page.
5. Wait until the initialising step is finished the
continue as below.
6 . Select your model of phone from the list that appears
7. Follow the connection steps that appear, ensuring that
you are holding the relevant button down before during and
after the connection phase until the update/repair begins.
I do hope this helps, let us know how it goes. 
I tried to back up my phone with PC Companion but I can't because it says I need to unlock my phone (I have a password set-up'ed) and the screen's all haywire.
Sony-Isa If you aren't able to unlock the screen then you will not be able to back up your data. I suggest skipping this step and going straight to Start under Support Zone with your phone turned off and not connected until you are prompted to. Unless you can get an OTG cable then you may be able to unlock the screen using that with a mouse also.
So I switched on my phone today and it worked just fine. I ran it through Diagnostics and it passed all the tests. I still not sure why the screen went "haywire" but I'm just glad everything turned out fine. Also, I want to thank those who helped.