Of course your driving instructor is going to put in a claim. Most driving instructors get a massive boner when this sort of thing happens. They don't earn much money at all and it is easier for them to be deliberately ambiguous when it comes to sorting out the special damages aspect, much like taxi drivers. Furthermore, they are conversant with the workings rather farcical small claims world.
When you claim for an injury, the claimant's insurer will add you to a database called CACHE PI/CRU. Driving instructors and taxi drivers often have multiple matches on this database.
I can't say much about your injuries but if you do decide to claim, don't be a bitch and go through one through one of those leeches of no-win no-fee solicitors (Minster Law, Silverbeck Rymer, Bromiley Holcroft etc). At least approach the other person's insurer to tell them that you are injured and see if they are equipped to deal with you directly. Many insurer's have departments that can deal with third party's when they are injured, this ranges from arranging medical reports, sourcing medical evidence to negotiating settlement.
Solicitors hate this but at least this way you are cutting out predictable costs, conditional fee arrangements and success fees etc. Moreover, if the insurer can deal direct with you it is an activity that is heavily regulated and something that you can turn away from at any point so you can't really say that they are going to fleece you.
If you went through a solicitor you would vastly increase the claims cost (£800 and 20% of damages under £500, CFA, 12.5% success fee uplift, ATE premium which is completely unnecessary most of the time and more). Something costing £5000 could have conceivably been settled for less than half of that.
It's the solicitors that are disgusting. When they call you in their guise of solicitors it is clear that they are just interested in their own profits because it's easy money. They couldn't give a flying f**k about you. Most of them are not solicitors as you would imagine by the way, they are depthless underqualified para-legals that think they have an important job.
That's my 2 cents.