In this area (the shins) most patients present with varicose veins and spider veins and treatment follows evaluation for truncal venous insufficiency with Doppler ultrassound (Duplex) scanning. Once this is excluded, sclerotherapy is ideal and sometimes topical laser will treat them adequately.
Broken skin capillaries can be due to multiple factors including genetics, trauma hormones, aging and even sun exposure. If you have other veins besides capillaries then you should have a full venous evaluation including a venous reflux ultrasound. You should see a vein doctor.