Hi Emily
I'm 18 months into my TD and I understand how scary and daunting it is. Your car loan will have to be included as its a personal loan and not Hire Purchase which is secured on the car. That's good in a way as it means you have use of a car that won't be costing you in monthly payments - a good trust deed company will allow you to keep your car provided (1) You need it to commute to your place of work and (2) It isn't a ridiculously expensive luxury limo or supercar. Regarding your mortgage, I think a credit search will only be carried out if you were re-applying via a new lender. If you are, like me, about to come to an end of a fixed rate period then your lender should contact you about what rate they can offer you but your not taking out new finance, simply switching from one mortgage product to another.
Hope all goes well and things get sorted for you soon.
S.C.