I got into a car accident, should i go to the hospital?

about 2 hours ago i rear ended a car going around 25-30mph. it was an accident but completely my fault. i had my sweatshirt on my lap n it fell on the floor mat and got stuck behind the break pedal. i was in so much shock, the front of my car is totaled and was towed. the other driver i hit their car was barely damaged. but i feel very badly about it. i was not feeling any pain at first but when i got home the whole left side of my body started to ache. now my shoulder and neck hurt and i have a really bad headache. like 9 out of 10 pain wise. i was wearing my seat belt. i feel very depressed and feel terribly for the person i hit. should i go to the hospital for the pain or wait it out till tomorrow?