OP, day 3 testing doesn't have to be done on day 3. It is baseline testing before starting another medicated cycle, and I had it done at SG on day 2, day 3, and day 4. In fact, for one IUI cycle I had (with Clomid), I was told that I could have gotten the testing done on day 5 and started meds that night, if absolutely necessary. I had to juggle 6 rounds of IUI with frequent work travel, and I'd wager only 3 of those rounds was I actually in for "day 3" testing on day 3.
See this thread from yesterday:
http://www.dcurbanmom.com/jforum/posts/list/606942.page
Also...if you saw a faint line, yes, you're pregnant. A line is a line. PMS symptoms, or "feeling your period coming" can also be signs of early pregnancy. They can also come from progesterone support, if you are currently using progesterone. Wait on that beta before ruling yourself out, and good luck!