Why do I have visible blue veins in chest and upper arms?

Some
cursory online research would suggest that there may be a connection between
spironolactone use and spider veins, but there has been no substantial evidence
that would indicate causation. The presence of spider veins is largely genetic,
but may also be affected by hormone production, obesity, and the use of various
medications. The good news is that spider veins are usually manageable with the
right med spa treatments. Speak with a cosmetic surgeon to get a better idea of
which procedure would be best for your needs.

Thank you for your question.Thin skin on the chest and breasts is a common underlying feature in patients that have varicosities in the chest area.Upper extremity veins are prominent in those with lean bodies with small body fat %, common in those that lift weights, and can occur in certain pathological conditions when there is proximal deep vein clots. BestDr Karamanoukian

Breasts veins are a common concern of many females.  I doubt that they are related to your medication.  The most common cause of breast  veins are aging, genetics and hormonal changes. Rarely, these veins can be due to underlying medical problems. Breast veins can usually be treated by sclerotherapy.  Upper arm veins are usually not treated but there causes are similar to what I mentioned.