Mazal tov on your recent wedding!
It is fairly common for a couple to need some time and practice before consummating. At this stage, however, we think it would be helpful for you to discuss the difficulties you have experienced in more direct detail, either with us here or on our phone hotline. Sometimes a small adjustment can make a big difference.
If we understand you correctly, your bedikot have been clear. Following the bedikot you see red blood. The blood you see after the bedikah may not affect your clean days, depending on where you see it and its size. For example, if you find it on your undergarment and it is smaller in area than a gris (roughly the American dime or Israeli shekel), then it does not invalidate the clean days and you may continue. To provide you more guidance, we would need more information about the blood quantity and where it is found.
Based on your description, it sounds very likely that you have a makkah, a wound, in the vaginal area. You could try looking in the mirror to see if you can locate an irritated external area that bleeds on contact. Also, seeing a physician for an exam might help you both to address this bleeding pattern and to receive information related to intercourse.
Please be back in touch with more details, again here or on our phone hotline.