So, are you wanting to get pregnant? If not, you need to buy some condoms asap or go on the pill. This is not wise to have sex like this unless you are trying to conceive. Urinating after sex will not do anything to prevent pregnancy nor will the pull out method.
So, couple of things. You did have sex in a window of time in which you could have gotten pregnant. This doesn't mean you did though and time will tell. The first day of your cycle is the first day of your period. You count from there. Most women are more fertile from day 9 to 20. BUT, you can get pregnant any time during your cycle when you have unprotected sex (as well as exposing yourself to std's). Here are my thoughts on your specific situation--- the second time you had intercourse you had heavy bleeding. That was probably your hymen breaking all the way. Women can bleed and quite heavily at that time. Your issues of vomiting and nausea, etc. have nothing to do with pregnancy. Symptoms of pregnancy do not start immediately. We have symptoms when pregnant because of the hormones the pregnancy creates and they take some time to build up. So, things like nausea/morning sickness usually begin on average for women around week 6 to 7 of pregnancy. You're also going to be experiencing pms around this time too if it is a week before your period.
Wait to see if your period shows up. If it doesn't, take a home pregnancy test using first mornings urine. If it is negative, do not test again until a full week has passed. If still no period, test again. good luck