Should have been primed with a shellac based primer first to keep the wood tannins from bleeding through.

Just more proof for me paint and primer combined is a ripoff.

Hollysprings nailed the cause.

The remedy is to use an oil based shellac primer(I prefer BullsEye 123 over Kilz from experience) and repaint with regular paint.

You might be able to use a water based Bullseye, but the oil based has never failed to protect for me---and I have painted pine knots that were oozing sap(enough to feel) and were sealed.

#1. used water based paint.
#2. problem. You used Behr.
#3. Should have used a coat of polyurethane or oil based sealer to seal the wood before the paint was ever applied.

Since most beadboards are made of cedar or pine. It acts as a sponge when water based paints are used. The rosin/pitch/sap will continue to bleed through the paint until it is properly sealed with an oil based product.

I learned the hard way too, only with bedroom trim painted white. When it came time for the kitchen remodel and bead board ceiling (and walls), I used the shellac based primer. So far, so good and it's been three years. I have yet to tackle the job of going back and sanding all the yellow spots on the casing and baseboards in the bedrooms and re-priming/painting. ugh.

Thanks everyone. @hippy what brand of paint do you recommend after? (Preferably affordable)

my two cents...I am no professional...what I know I learned from pop, a union painter for 30+ years..

#1. used water based paint.
Not sure if he was referring to just the primer. Do they even make oil based paint anymore? Pop loved it back in the day, especially for primed wood trim...very durable...ironically, back in the day, eventually the molding he used it on yellowed for me after a number of years. Currently I use/used bulseye water base throughout my house.

#2. problem. You used Behr.
I won't start this debate up again. I used Behr thru my whole house...no problems. Think of how many gallons are sold; and its $25+ a gallon...not super cheap.....if it was crap it would not be sold. Pop used to say the prep was more important than the brand. I don't buy into the all in one paint....no matter what brand though...

3. Should have used a coat of polyurethane or oil based sealer to seal the wood before the paint was ever applied.
No idea...I'd have used the bullseye...maybe my ceiling would be yellow too! Not sure...I have primed exterior wood with Bullseye and painted...no yellowing...

I'm a beginner DIYer I didn't know my ceiling would yellow. I feel foolish now but definitely learned my lesson. So it doesn't matter what brand of paint I use as long as I use a good primer/sealer. Would zinsser bin be a good choice?

You do not need Bin which is shellac based and very expensive. Just get Zinsser's odorless Cover Stain and problem solved. It matters not what you put over it, although Behr would be my very last choice.
Somebody up there said oil based shellac and there is no such thing

Poly will still pull sap through from knots, as poly is oil-based and had mineral spirits. That's why shellac has been the go-to for sealing sapwood and knots from a century +.
Other problem with poly is of course nothing sticks to it, not even more poly, so you'd have to rigorously scuff sand, So IMHO, really bad advice there.
Casey

I should have written shellac based primer---NON water based.

BIN is expensive by the 5 gallon, but not by the gallon, considering the amount of work it eliminates and the almost lifetime protection. Plus, BIN is thin enough to not fill in the groves in the beadboard.

BIN is an interior primer, so if that ceiling is on an outside porch, the correct primer(from Zinsser) is Bullseye.

Kilz, in my experience is a second class stain blocker---way too thick for detailed paint jobs, like beadboard.

Paint is another entire bees nest of opinions. I personally prefer Sherwin Williams. However, when it comes to interior ceiling paint, one brand is just one brand. Interior ceiling paint has the least wear/tear and only has smoke/etc. as a weathering agent. Most folks never notice how a ceiling darkens unless there are glaring differences.

Bin = $42 per gal

cover stain=$21 per gal

@ home depot

The beadboard is interior (bedroom ceiling) I have some BIN already, how many coats of BIN do I need to keep anything from bleeding through again? What type of paint would be best as a top coat after the BIN is applied? I've learned my lesson with water based paint! Sorry if I'm asking too much I'm not too familiar with which paint type goes best with what!

If you have the BIN, go ahead and use it. One coat is all that is needed You can put anything you want over top. Follow directions on can, especially drying time. Personally, I like PPG Manor Hall

White shellac stain-blocker also comes in an aerosol spray can; it's what we always use while backpriming pine for woodwork. We hit the knots and sap streaks on a bunch of planks, then start priming; by the time we finished spraying the last knot, the first knot is dry. Even if Polyurethane did block knot-bleed, which it doesn't, you would have to wait some hours, if not a day to coat over it, and there's still a risk of poor adhesion.
Casey

Should I just put the shellac over the spots only or go over the entire ceiling?

as I said
If you have the BIN, go ahead and use it.

just do the whole ceiling

Thank you!