I dunno about a "swollen" achilles tendon, but I sure do know about how
much they can hurt.  I have psoriatic arthritis, and one manifestation
of that for me is achilles enthesiopathy.  Hurts like a sonnovabitch, so
I feel your pain.  Exerped from this website,
http://www.wsiat.on.ca/english/mlo/plantar_screen.htm which is a fairly
good explanation of heel pain, is a description of enthesiopathy:

"Pain at the sites of tendon or ligament insertion (enthesiopathy) is
often observed in patients with seronegative arthropathies [5]. Clinical
syndromes such as ankylosing spondylitis, psoriatic arthritis, Reiter's
syndrome, inflammatory bowel disease and Behcet's syndrome must be ruled
out. Associated complaints such as skin lesions, conjunctivitis,
arthritis, back pain or abdominal complaints should prompt a referral to
a rheumatologist. Screening tests include antigen-B27 (HLA-B27) and
sedimentation rate (ESR) can aid in the diagnosis"

I did some physical therapy for a while, which was both helpful and a
real pain.  Remember folks, when the therapist taped up my heel.  Holy
crap, was I miserable.  But, I think it may have helped in the long run.  
Ooooohhhhh, bad choice of words.  Anyway, learn stuff and follow your
doc's advice.  If it doesn't help, get a second opinion.  Heel pain
sucks.  It's one of my biggest pains these days.