Texts Read Online? Can You?

Hi! I was just wondering if you can check and read received and sent text messages on any particular website. Like, for example if I sent 100 texts and received 75 texts in like a certain period of time, could my parents have found a website to where they can access my phone number and read all those texts ? If anyone knows of any website where you can do this, can you please tell me what the name of the website it is? And if there is no possible way that my text messages could be read.. then please tell me to relieve my worries. Much thanks to those who can help

if you send the messages from vtext.com (verizon's text website), you can retrieve them on there (and any responses) within 5 days or so. If not, the messages only go to the handset they are sent to.