I'm assuming you haven't seen a doctor about any of this. In this case, first of all please do make an appointment and talk to your doctor as soon as you can. If for nothing else it will ease your mind. This is what doctors are for, to help you. Please consider this.
Please understand we are not medical doctors here either, so we can't tell you exactly what is going on either. But we can tell you that yes it is possible that you have a STD. You rubbed your penis unprotected, against her vagina. That is considered sexual contact and can spread diseases. BUT that doesn't mean you do have one.
The clear liquid could be pre-ejaculate. As it is normally clear. But once again it may not be. Bladder infections can cause your urine to dribble out as you explained, but once again could be something else.
I would guess from what you have explained here your doctor would ask you to come see him. It could be nothing much or it could be a problem he may be able to fix or at the least start treating.
Best advice, call your doctor and have your self checked.
Welcome to the boards and hope to see you again with some good news!!