It has almost nothing to do with bitcoin cash. Segwit activation is the first step towards adding new features to bitcoin - it doesn't magically speed up all transactions just by being activated. Next all exchanges, wallets and service need to start using segwit transactions for it to actually ease pressure on fees and block sizes. So far only very few segwit transactions have been made as most transactions are still normal transactions and they do not get faster or cheaper just because segwit is activated.
On the other hand what you're currently seeing with fees going up and transactions being delayed is a concerted spam effort coordinated by people trying to make it look like the bitcoin blockchain is congested and needs a controversial 2x upgrade in November which is being pushed by the NYA miners when most of the userbase and developers are against it and will not agree to their threats. It's artificial and does not represent the real economy situation.
Hope all that's written in this comment is true. Bitcoin Cash and the problems of the high transaction fees came at the same time. Bitcoin have to solve the issues of their transaction fees, or else will let Bitcoin Cash emerge, because the ones that are behind it are making everything to not let it dive like another altcoin. And f these transaction fees happen to get higher, people will also start to change to Bitcoin Cash, making it grow in value and threaten bitcoin's value.