So, first things first. Morning sickness doesn't happen as early as two days after conception occurs. Most women experience morning sickness 4 to 6 WEEKS after they conceive. The mind is a powerful thing, and often times, merely thinking about something can cause the symptoms to appear. The vomitting could have simply been a stomach flu of some kind, or your worry made you throw up the way you did. Back pain could also be something that you're bringing upon yourself.
Of course, it is possibly, and I'm not eliminating the chance. Some women do continue to get their periods despite pregnancy. Your best bet is to go to a doctor and have it checked out. This way, if there's some other complication that's causing these problems, you will know it.
The reason for this, yellow like discharge can be a sign of a color, especially if you've noticed a recent change. It's possible that it's a yeast infection, or other such problem. The stomach cramps could also be another sign. Just so you know, slight cramps can be common in pregnancy, but severe cramps that hurt can be signs of something serious (pregnant or not) that need to be looked at (such an ectopic pregnanct).
And note any other changes that you may know of. Is your period or bleeding heavier than normal? Or is it light like spotting? The more you can tell her, the more she can do to see if everything is alright. Unprotected sex can not only result in pregnancy, but also transfers of STIs (or STDs). So it's best to get it checked out so that a doctor can tell you if you alright, and if not, you can get something to help treat what you're feeling :).
Best of luck to you, and just go to the doctor and get it checked. It's better safe than sorry, right? It's better to go and have her tell you everything's alright, then to not go and find out things have progressed too far.