Sounds like you may need to have the vet back to take a look. The first thing I'd look at for his eyes--are the lashes okay? If the eyelids happen to be inverted, the lashes will be rolled in against his eyes, & that will cause intense irritation--watery, red eyes--if that is the case the lids need to be rolled out, so get the lashes out & away from his eyes. Sometimes once with fix them up; sometimes they have to be rolled out several times (& I try to wipe them dry, that helps them to stay out where they should be. Left wet they are sticky & are more inclined to roll in again.
I haven't had a septic foal, but my vet book does say that the eyes of a septic foal will often look grey-green, due to white blood cells in the ocular fluid. But, if the eyelids aren't inverted, definitely the red watery eyes are a cause for concern.
As for the red tongue, yes, that's not a good sign. How red is it though? Bright red? Red-purple? Quite pink, as in bright pink?
If your foal is shivering, I'd be concerned about that. I don't like to see new foals shivering. Is he inside, if not in a stall then at least in a shed? Out of the wind (if there's a wind/breeze?) ? If he's outside I'd get him in somewhere that is sheltered. If he's inside now & shivering, I'd fix up a blanket for him. If you don't have a foal blanket you can use a child's sweatshirt or sweater. Or if you have a fleece or wool blanket you can cut down to size, quickly cut out a little horse blanket--a quick row of stitching will close the front, make a little surcingle out of the same material, wrap that around & duct tape it. This works good--been there, done that!! (This year I am much better supplied in foal blankets of all sizes!!) --you can fit the blanket snugly so that it will keep him warm & he won't get his legs tangled up in the chest or surcingle of the blanket.
But, in any case, do make that call to your vet & get his opinion on this foal's condition!