I have been in the same position, I ran to the ER,and after running blood tests and everything I was fine baby was fine. However, the bleeding never stopped and the vaginal ultra sound they gave made it worse...stop having sex...it's not worth it...and also see if u can get progesterone shots....usually bleeding can occur because the placenta is having a hard time latching. Don't listen to the it's normal...because I did, and after two miscarriages I have learned to stop thinking it's okay.....take folic acid...separately from ur prenatal, and if u take vitamin c at a high dose...stop. have blood tests to make sure ur levels are still high, but ask for the progesterone!!!!!
If the blood is bright red and you are cramping then it is possible bad news. Brown blood is old blood from the implantation. Possibly the Intercourse helped it exit your body.
Do not stress just yet. Spotting is very common in the first trimester. If you start to cramp and bleed more I would suggest the ER.