Your discharge is normal, as the pill has hormones that your body is adjusting to. Your period may become lighter and shorter as well.
You said you've been on the pill for just over a week: when did you and your boyfriend have sex without the condom? I believe bc becomes effective (generally) after one week on the pill.
As for your burning sensation...Were the condoms you used lubricated? One reason for foreplay is to ensure that the woman's vagina creates lubrication (and it's fun too!). If you were not "wet" enough, you might have caused some irritation or slight tearing. It's nothing to worry about right now. The burning should go away on its own, but just take it easy for a few days (i had this problem for a while when I first starting having sex). You might want to try buying a lubricant. I recommend astroglide (i do not recommend the "warming" lubricants).
But if the sensation doesn't go away, go see your doctor.