Was the journey on a weekday or at the weekend? A Network Railcard has a minimum discounted fare of £13 on week days so there would be no discount available on a journey between Reading and Reading West.
For a £2 ticket? That's extremely disproportionate. Also me having depression and anxiety means that I am unable to function as normal. I don't think this is right. I will appeal.
I am sorry to hear about your depression and anxiety. The thing that GWR will focus on is whether this impacted your ability to select the correct railcard.
I don't know which ticketing site you used but if it was Trainline then Network Railcard and Job Centre Plus Railcards are in different parts of the railcard drop down list, so how did you accidentally select it? If GWR look at your ticketing account will they find other tickets purchased with a Job Centre Plus discount applied?
There is no right of appeal as such. Based on what you have told us there are three possible outcomes to this:
1. GWR prosecute you in the Magistrates Court. This is unlikley if you co-operate with them
2. GWR offer you an out of court settlement. You pay them some money and in return they don't prosecute you
3. They take no further action. My view is this is unlikely
If the case does end up in court then all GWR has to demonstrate to the Magistrates is that you didn't have a valid ticket. However harsh it sounds, you didn't have a valid ticket.
Let's not get ahead of ourselves. Wait for the letter to come from GWR.