Maybe write down what is going on; it may be easier and then if you are really nervous at the time and find you can't talk then at least you have it written down.
I'm glad you're planning on going and they won't think it weird at all that you didn't at first, MANY don't, possibly more than those that do as it takes a lot of courage. The best thing may actually be for you to go to your local sex health/ STI clinic. They're usually places where you don't have to book an appointment and can just go down and they will be used to this, keep everything confidential (though your doctor will also do this) and at least it gets it out of the way. A quick google search and you should hopefully be able to find your local Sexual Health/ STI clinic. If you go they won't judge you in any way at all and yes, it may be psychological but that is not stupid at all as what you've been through is something noone should have to and this does leave psychological problems and some of these can cause the muscles in your vaginal wall to tighten and things but there could also be physical damage done such as any healing could have caused the area to tighten up due to scarring along with other forms of damage.
They will not get the police involved. They'll ask if you want them to be because if so at least they've got it written down as proof you've been, got checked out and what you've said and they can arrange that for you. I know for some who've been raped going to the police can really help as a closure to it all even if it doesn't lead to anything (though hopefully it would).
They will look for any damage done and also any signs visually of an STI. Swabs will look for Chlamydia, Genital Herpes, Gonorrhoea and Syphilis. Chlamydia is a bacteria and up to 1 in 5 people young people are infected by it and can show no symptoms but can lead to infertility though is easily treated with a course of antibiotics.
Blood Tests will look for HIV (which may require 2 tests 12weeks apart depending how long ago it was) along with Hepatitis B & C which can all be life threatening and make you really really ill so it is worth getting checked out.
This link gives you more info on STI tests and as well as that if you scroll down on the right there is an area where you can put in your post code and it will come up with your local GUM (STI) Clinic.