Head Injury, Dizzy, No Bleeding. Headache, Painful. Should I Get A CAT Scan?

Question: I am a 24-year-old female, 5'5", 128 lbs. Last night around midnight, I was at a friend's house where I was sitting on the floor and somehow trashed my head back into the futon's pointy, painted wooden armrest (like a two-by-four). The sharp part hit the part of my head just above the neck where there is a round jut-out from the skull. It hurt quite badly and I saw stars. I felt a bit dizzy but I did not pass out and I did drive home. I told my parents, who I live with, what happened. We iced it and they checked my pupils (which were normal) and examined the back (the skin was not broken; no blood) and I became extremely drowsy before falling asleep around 3:30 a.m. I set an alarm for 6:00 a.m., just to be safe, and I was able to wake up just fine. Today, I still have a big reverberating headache in back of my head at the site of the injury and I have been sleepy and napping intermittently all day. I am slightly dizzy and feel a little foggy/"off," but am obviously coherent enough to write this to you. It hurts a bit to hold my head up so I'm thinking it may have slightly affected my neck, as well. I am due to leave on a cross-country train trip on Thursday and am very nervous about the possibility of an unattended "brain bleed"! Should I go to the ER and/or get a CAT scan? I'm nervous but do not want to waste time and get irradiated for nothing. Please, please advise. Thank you!