This does indeed sound like whiplash. Basically, whiplash is a strain or spasm of the muscles that run up and down the sides of the spine in the neck. It is caused by the sudden back and forth motion of the head and neck that occurs when you get into a motor vehicle collision.
Generally speaking, whiplash symptoms are not too bad immediately after the accident. In part this is because the stress of the accident and adrenaline tend to keep the symptoms at bay. However, on the second and third day after the accident, the stiffness and tension in the muscles does tend to become much more apparent.
If you think you are suffering from whiplash, the first and most important thing to do is to go see your primary care doctor
for an evaluation. They will be able to examine your neck closely to make sure that you did not sustain a more serious neck injury
during the accident. Assuming not, they will be able to make some recommendations about how to treat the pain and stiffness. Typically, this includes anti inflammatory medications such as ibuprofen or naproxen, rest, and heating pads. Sometimes, physical therapy is needed to help improve mobility and get you back to feeling normal.