I can't say I know how you feel (I have fried eggs!!).
But I LOVE the yoga poses.
Perhaps speak to the instructor and see if they can suggest anything? Or practice at home to see if you can get used to it? I would hate for you to give up as the benefits will soon show.

Everything you all are sayng is so relatable!
I feel the same with I do downward facing dog. Actually, when I do any sun salutation, I feel nauseated. But I guarantee if you keep moving on, you will feel better each time.
Oh yes, and a good sports bra (I wear a running bra--Moving Comfort (I think) is the name brand.) is a must! Good luck and namaste to you.

I have big boobs too and I find that a very secure sports bra is key. I like the Moving Comfort Fiona, the Anita Extreme Control and the Goddess sports bra. (The latter two have a much wider range of sizes, in case the Fiona doesn't come in your size.) I'd also make sure you are wearing the correct size. In all my years of activities, I've never had my girls slip out the bottom of a sports bra.

I started a yoga class last month. I've been to it four times so far and I'm not sure I can keep going. My problem is that damn downward dog thing. Even the child's pose, which is what I'm suppose to go back to when I need to rest, kills me. The problem I'm having is all the blood rushing to my head, making me feel sick. It's as though my head hates to be lower than my heart. Or maybe it's that my throat hates to have my breasts shoved up into it. I have big breasts.

Anyway, I'm not giving up yet. I've been reading about modifications of the downward dog. Hopefully, I'll get the hang of it eventually.

Boobs + yoga requires a LOT of self-acceptance. When I get into those poses where I feel like by boobs will suffocate me I used to get very frustrated. I blamed my body, and myself, for having all that flesh in the way. (boobs AND belly, ugh and my thighs lol) and I let myself feel frustrated instead of accepting that this is my body right now, and I've got to work with it. I can work towards change...but right now, this is what I have to work with.

Read this recently: yoga is tolerating the consequences of being yourself.

Child's pose used to be torture! Being top heavy meant that my face would be mushed into the floor...to modify I made fists, and put one fist on top of the other on the floor in front of me to support my head, which allowed me to use my arms and shoulders to support my upper body a bit and provide some space to breathe. (This should also help reduce the head-lower-than-heart problem a little) Eventually I only needed one fist, now I can usually rest my head on the ground. Also, separate your knees (but keep feet together) to make room for your body if you feel squished against your thighs. Lastly, don't feel self-conscious if your butt is up in the air instead of pressed down on your heels lol.

There are several poses that create that suffocating feeling if you have large breasts: plow, shoulder stand are "basic" for most people but for me it's always a bit of a fight. I breathe slowly and remind myself that as long as I can take in air, the discomfort is temporary. I actually find that bra choice is important here. A sports bra that creates a bit of uniboob is worst, because when my neck is bent, I'm breathing into that tight fabric...but a bra that separates my breasts, um...lol allows me to have my chin between my breasts where there's a little space. Sometimes, before one of those poses, I actually adjust my girls to either side a little. Or sometimes, when it just can't deal with it...I do an alternate pose...or I do the pose just for 10 seconds. Or I don't do it at all, I take a breather.

For downward dog...work on trying to lengthen your spine, all the way from your tush to your skull. Work on literally making your body longer in the pose to create more space. If you need to look up a little to get some space, that's ok too as long as your neck isn't strained.

Most importantly...have patience. If you actually do not like yoga, don't force it. But if you like it and just find you are struggling in some types of poses well...that's kind of the point. You learn to breathe and find peace in your mind, even when you are uncomfortable...and this skill translates very well into life outside of class.

Maybe you've already been told/shown these things so I apologize if I'm telling you what you already know. I admit I get a little evangelical when it comes to yoga!

ETA: I know the post is a bit old...but not so old as to be irrelevant.

Best advice I've gotten with yoga was to "Push to Your edges, and no further" Like, legit, there comes a point where downward dog is the most comfortable resting position in the universe and you'll wish you could do it at any point in time without strange stares....but your body has to get there first.
Find your edges as you go, does this feel uncomfortably tight?
If I go further will this be pain, or am I just reaching My Edge?

Next class focus on your breathing and when you find those edges, back off just a bit.

Hope that helps!