What does travel have to do with it?

Perhaps long periods of sitting on a flight?

If you suspect this is happening to you (all of the sudden you can't really breathe), is there anything you can even do? Or just hope it's not bad enough to be fatal?

Go to a doctor right away. There are anticoagulants which can dissolve blood clots and/or ways of physically preventing the clot from reaching the lungs.

Also an ounce of prevention: avoid extended sitting; exercise regularly.

https://www.webmd.com/lung/tc/pulmonary-embolism-treatment-o...

https://www.mayoclinic.org/diseases-conditions/deep-vein-thr...

If you experience sudden shortness of breath, call 911 (or whatever your local emergency services number is).

Taking aspirin might help, although there is no published evidence:

http://emj.bmj.com/content/22/5/365