Can there be any medical reason why you would get cystitis and piles at the same time?

Sure: Piles or hemorrhoidal swelling is caused or aggravated by anything that causes one to increase straining, particularly with bowel movements. Dehydration can cause constipation, which can be associated with cystitis. Many medications taken for cystitis can also cause constipation or loose stools, both of which can aggravate piles through straining at the toilet.