Are you 8 weeks 4 days just counting from your last period, or did you get an ultrasound and the doctor told you this? If so, did the doctor give you an estimated due date from the measurements of the baby and its developmental markers, or is this all just counted from the first day of your last period?
(By the last, I mean, did the doctor simply ask you when your last period began and then use a little cardboard wheel to tell you how far along you were?)
OK, well, sex 6 days apart is pretty hard to separate, but you might be able to find out from the doctor if sex from some other time than those two times could have produced the pregnancy. Are your cycles super regular, and how often do the periods come? Have you had sex with anyone else besides those two times?
There are two things you could do before the baby is born to know who the father is. One merely "might" help and the other would be certain but it costs a lot of money. If you don't do either one, you can do a DNA test after the baby comes, and you should test with both guys. 6 days is pretty darn close together.
The first thing to try is to get an ultrasound immediately (that is, at your appointment on the 23rd, no later). Don't tell the doc you know when your last period came (or you could say it is so irregular you don't want to use it to determine how far along you are). Ask specifically for an estimated due date from the embryo's measurements as shown on the ultrasound. You can take that estimated due date home and put it into an online conception calculator (or simply count back from it 266 days on a calendar) and that will give you an estimated date of conception based on the actual baby's measurements. If you are really lucky, it will point to one guy more than the other. But you are a little late to try this method, it is more exact earlier i pregnancy (like, your 6th or 7th week).
The other thing you can do before the baby comes is a prenatal DNA test for paternity through Ravgen or the DDC. These are very costly but if you test with both guys you will get a certain answer.
If you don't get an ultrasound this upcoming week (I would insist or find another doctor, in your shoes -- the timing is that important), and if you can't afford a prenatal test, get a post-natal DNA test with both guys. They are only about a tenth as expensive, and they are also the only paternity tests the courts will accept when it comes to child support.