As a recent survivor of numerous leg and lung blood clots numerous times in the last 6 months, plus the almost always fatal Pulmonary Embolus, I will tell you no: a dog can't be trained to detect them. At least at this point in time.
I am disabled by blood clots.... and many other things.
The symptoms are either absolutely none (and one just keels over), or the symptoms are extremely pronounced and detectable by one's self or even people around them (gasping for breath, excruciating immobilizing pain, sweating, wheezing, massive swelling of extremities, collapse, death)
One can teach response, rather than alert - because no alert is necessary - - - one knows when they are dying (at least if they are awake).
One might teach the dog to pull an emergency cord to summon paramedics (available in some housing), bring the cell phone to you, have an emergency SD phone the dog can push the button for help, or even have a panic button the dog can press. (similar to screamers truckers use to wake up from sleeping). Teach the dog to keep nudging, pawing or licking the person down in an effort to keep them semi-roused as long as possible while waiting for paramedics.
Keep specific ICE info on your dog's collar, vest and harness, and on your person, and on the fridge for paramedics to prevent delay of treatment.
I am trying to find a GPS locater my dog can operate as I am still running around like a crazy teen trying to cram as much fun - joy - wildness - helping others as I can before I die. (Also, if I keep busy maybe the Grim Reaper or the Devil won't be able to catch me!)
I now have an aneurysm in my spleen at risk for rupturing in addition to repeat bouts of blood clots. I am on Xarelto and Plavix plus Quinnapril and Bystolic, and am being tested for blood cancer because I have 3 abnormal markers out of 5 re: blood cancer. <sigh>
I wish you safety. I am very sad to hear someone just starting life has to go through such a rugged diagnosis, that can be quite frightening and sobering. Hang in there! Sounds corny: but think positive and determined and focus on living life on your terms and speed. (I'm on warp speed now)