the most effective long-term solution is to make your hsuband unclog it.

just sayin'.

I'm afraid this is all "my problem."

The hardware store is your best friend. Since access was through a very restricted drain (stupidly installed 15 years ago), I chose a flat plastic drain snake. It's about 30 inches long, flat plastic, with spines on either side. You shove it down, it's flexible enough to go around a few corners, and then just shove through the clog. Run plenty of water through afterward, and since your clog is lint and Kleenex, make sure it's hot water.

Then, since you drain your washer into the sink, put some old pantyhose on the end of the drain pipe to collect the pocket detritus. Just put about half a leg on and secure it with a rubber band. When it gets full, find another leg and replace it.

ETA: while better living through chemistry will get through minor clogs, there's nothing like a snake for a bad one. My own chemistry is Kosher salt, baking soda and vinegar. If that doesn't do it, it's time for the snake. Since I process raw fleece, that time comes frequently.

How much of each of the salt, baking soda and vinegar in the mix?

Salt goes in first, then baking soda, then vinegar. It fizzes and foams and will push a thin clog on through. It won't work on a bad one and your best strategy for Kleenex in pockets is to put that piece of pantyhose on the drain.

I say this as someone who does that for processing raw fleece in the washer.

Should I try again?

It won't work if you mix it in a bowl. The idea is to get the salt and baking soda down the drain as far as possible and then pour in the vinegar to react with the soda to foam the clog out.

As I said, it won't work with big clogs and yours is likely to be a big one. Get the snake.

Plumbers hate that stuff to be used before they come to snake a pipe. It splashes in their face and eats their tools.

Should I wear rubber gloves?

The drain is slow but eventually the water goes down. So some of it must have been cleared.

I just don't know why the coathanger with hook at end didn't yield anything...I pushed it down the length of the pipe and did that several times hoping some of the kleenex would be "coughed" up...

If you can't get it, maybe a call to a handyman might work. Plumbers and drain services can be expensive - around here $200 bucks just to show. I have a couple handyment that will do a service call for $60 bucks. If you can find one proficient with a snake it might be worth it.

I've tried messing with those snakes. There is definitely a bit of a learnig curve so I never had any luck.

The last time I hired a guy he had one attached do his drill. I think power is the way to go. The pros use those larger set ups - which can be dangerous to the non-skilled. I've heard of guys breaking their arm using one.

Great idea about a handy man. I just had one doing some retrofitting of my house to make it more accessible when my husband gets out of rehab. He'll be by this afternoon.