Welcome and thanks for your question I am Dr. German I would be here to help you and give you assistance until you are satisfied, yes ,the rash is caused by the irritation loose stools produce on the anal skin .
There is no need to worry , your symptoms could improve following simple recommendations including :clean the area with warm water and soft toilet paper , you could apply petroleum jelly or a mild hydrocortisone cream which you can get over the counter not longer than 5-7 days , drink plenty of water and eat high fiber foods specially fruits , vegetables and whole grain cereals . Avoid irritants specially spicy foods and wear loose cotton underwear .
With the vaginal discharge , an infectious process is probably the main cause . At this moment , if you saw small blood stains even if you only saw them the first day a Pap Smear should be performed to investigate the presence of cervical cell alterations or dysplasia , other conditions will need to be investigated including : a bacterial infection like Gardnerella Vaginalis , STD's like Chlamydia or Gonorrhea, parasite infections like Trichomona Vaginalis or fungal infections like a yeast infection .
Your doctor will be able to determine which of these conditions is producing your symptoms after he performs a vaginal culture and a Pap Smear ,so he can give you an appropriate treatment.
In the meantime, maintain the vaginal area dry and clean , do not douche , use a gentle mild soap , eat unsweetened yogurt or get acidophilus tablets and avoid using fragrance ,powders and sprays in the area .
If you need any additional information I will be happy to continue further and assist you until you are completely satisfied .
Good luck to you and have a good day ! Please leave a positive feedback ( click on excellent or good service ) if you are satisfied with my answer.