A shellac based primer will cover the knots but that’s only part of the problem.

The T&G really needs to be replaced. Find a material that's free of knots, finish prior to install, and no caulk.

And T&G isn't a good choice where the cabinets go to the ceiling. Notice how it looks in your first image.

Unless the tongue and groove can be replaced without taking the cabinets out, that isn’t an option. We didn’t choose the wood, we thought the contractor knew what would work since we asked for it to be painted. I agree, but I didn’t know any better about not doing it with cabinets to the ceiling 😭

The knots will blead through no matter what you do, and the wood will expand and contract. That is what a wood ceiling does. The amateurish caulking at the end joints is ridiculous and needs to be removed.

I would remove the ceiling, and put new sheetrock up, tape, it mud it, etc and then primer it and give it two coats of white paint. Yes, I agree, its a terrible looking ceiling.

Maybe having lived in an antique home I’m not upset with a T&G ceiling but i am upset with the installation. I would make the contractor hire someone to redo the ceiling joints properly and then hire a professionsl painter. I think if redone well you can happily live with it.

Drywall.

I can't afford to remove the cabinets and redo the ceiling to do drywall. Wish I would have gone with drywall to begin with.

You could have thin drywall put over the top of it, and right up to the cabinets. A good drywall person, could do that without anyone ever seeing that it doesnt go under the cabinet tops.

Tongue and groove ceilings are beautiful, if done with the right wood. Nothing wrong with them, but, yours were not done with the correct type of wood, although, even that would have been ok, if installed corectly. Its unlikely, that anything can be done to make what you have look any better, unfortunately.

I caulked and painted a knotty ceiling; no knots showed through for at least a decade.

I imagine your contractor bought the least expensive T&G they could find and then did a poor install.

I see evidence of face nailing and tear-out from the milling process.

T&G installed like this is often end matched.

Is there drywall under the wood? Is there any living space (2nd floor) above?

End matched not available in my market ...

There is a ceiling under the tongue and groove. It is the old square tiles that were used back in the 50's. There is a small room above that isn't used for anything, just attic space.

Was your house plaster? If so, there could be a plaster ceiling under those ceiling tiles. Ceiling tiles became popular in the 70's, and people put them over the top of original ceilings. Those ceiling tiles, usually contained asbestoes too.

I can't afford to remove the cabinets and redo the ceiling to do drywall.

Don't have to remove the cabinets. Remove the crown moulding, cut the T & G flush with the front of the cabinets, remove the wood ceiling (leaving the wood that is over the cabinets) and install drywall. When the crown is reinstalled, it will cover the seam where the drywall butts up the the T&G.

If you can't afford to sheetrock it, then I'd get up there and sand those badly done joints until they look good. Then I'd paint the ceiling myself. There's truth in the statement that if you want a job done right, do it yourself.

No, there wasn't any plaster. I think this kitchen was added to the house sometime in the 70's. It was originally a 3-room house, and that kitchen wasn't one of the original rooms. I think we will go with sanding or getting that caulk out, painting with a stain blocking primer, repaint and hope for the best. I appreciate all the suggestions and advice!!

This is my Airbnb. The wood expands and contracts with the seasons so we purposely didn’t caulk. This winter there were probably 1/8” gaps at the end of boards, this summer they will be tight. That’s what wood does. Sand, prime, paint. It will be great. But you have to embrace the knots and gaps when you choose a pine ceiling.

That is beautiful. Love the colors. I wish my contractor had chosen something besides pine. He probably chose the cheapest T&G. A learning experience for us. What type of wood was used on your ceiling?

There's several products that can seal knots but fixing botched joints is a story in it's own. It is far easier to do it right from the beginning so I seriously doubt they can do better the second time.

The knots would be the least of my worries. A coat of shellac and repaint, and they will be fine. It is the joints, that are a lot of work. They should not have been caulked. Wood expands and contracts, like Hallett mentioned above.