Looks like Scale IMO, a pest problem common to house plants and difficult to eradicate. They are actually insects although they don't appear as such.

Neem Oil spray helps but many recommend first cleaning the leaves with cotton balls dipped in a mix of rubbing alcohol and water 1 part alcohol to 5 parts waters.

I have no idea how well this will work on tomato plants, no personal experience using it on them, since they are not normally grown indoors.

You can Google 'Scale on house plants' for more info and lots of pics.

Dave

Hi. Did you ever find out what this was or how to cure it? I'm having the same problem and it seems to be rare enough that this is the only similar picture I can find on the internet!

Thanks!

It didn't look like scale to me. It looks more like edema caused by overwatering. Google images of scale. It looks more like little raised shells. It would be very unusual for a tomato seedling to become that badly infected with scale. I would destroy the plant if it had scale that bad.

IME, that is not scale... scale will be individual waxy encapsulations that actually house the insects.
This looks like edema to me too.