Yes a guy can feel a girl’s boobs when he hugs a girl but it’s not a classic ‘cop a feel’ maneuver, such as stopping short. The problem is that usually whatever the girl is wearing tends to block the direct feeling of the boobage.
It does sound to me like you must be very large proportioned if guys are consistently giving you side hugs (something I cannot remember doing even once in my life), perhaps that is the only way they can get their arms around your body.
Short of wearing 80s style spikes on your shoulders, avoiding side hugs might be a very difficult task. Have you considered not letting guys hug you at all?