Why do I have what looks like broken blood vessels on my shoulders from lifting a heavy object?

Bruise. A broken blood vessel causes bruising - extravasation of blood (blood coming out of vessel). Lifting heavy objects serves a stress factor for vessels as it causes pressure to build up in capillaries and if it is high enough to break the vessel wall, it causes blood to come out and build up under the skin causing ecchimosis or what we know as bruising.
It is possible. If you left heavy object with pressure you could rupture small blood vessel.