Unless you can prove it medically, beyond reasonable doubt, then no you shouldn't.
"Reasonable Doubt" is CRIMINAL proceedings, this is civil, and the test is on "Balance of Probability".
And we are talking about a rear end shunt here, not a murder trial, there is no doubt who hit who. Even on the balance of probability there is not doubt that who hit into the back of who.
And yes, i would claim.
Whiplash injuries that resolves within 2 years fall between 750 to £2250 (i think).
The steps are :-
See Solicitor
He writes letter of claim to the other side
(they should accept liability for the accident as it was a rear shunt)
He direct you to a specialist for an appointment
He gets medical report
(negotiates settlement)
Issue proceedings (the case will be arguing on quantum, not liability as that has been admitted)
(continue to negotiate)
You do a witness statement
etc
Trial (VERY unlikely)
If the medical report is favourable, i can't see why it won't be, then you should get offers from the other side to settle. If it is not then they might want their own expert, for a fast track case, which this will be. It is unlikely they would want to get their own expert opinion. It is more economical to settle this out of court.
p.s.
General Damages - Injuries
Special damages - quantifiable items - car, clothes, even a holiday that you've paid for but unable to go due to the accident.
pps
You have 3 years from the date of the accident to issue the claim. Or if you are under 18, then 3 years from the date of your birthday.