I have been in your boat on and off from 4 weeks-15 weeks, although it was particularly bad for a couple of weeks. Besides the breathlessness (even getting up off a seat is hard work!) I just felt like I couldn't get enough oxygen.
The best thing for me was working on deep breathing into my belly. Are you familiar with this? I was told by my osteopath that I do all my breathing into my chest which is not good for tension or for taking in enough oxygen. Mastering the belly breath has helped with my yawning and sighing, for sure.
Anyway it's best practiced laying on your back - practice a couple of times a day as not only will you feel better but you'll be able to do it more effectively when sitting/standing up. To practice, place a hand on your belly, maybe even two (one just under the ribs, the other above the pubes). Slowly take in a breath that makes your belly rise first, then you can keep the breath flowing so it expands the diaphragm and finally the chest. Repeat in reverse and breath out gently and fully so your tummy is quite pulled in. Then repeat a few times. The main thing is to keep it slow and smooth. It's often helpful to count slowly as you breathe in and out, eg count to 5 each way, and as you get more relaxed you might be able to make it to 6 or even 10.
Sometimes with yoga breathing you'll be encouraged to hold the breath for a few counts on both the inbreath and outbreath. My preggo yoga instructers say not do do this as we need as much oxygen as possible! So just keep it flowing.
HTH, let me know how it goes if you give it a try.
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