Hi, I was an IT consultant and avid reader of Wikileaks and DARPA's unclassified project records before the crazy took over.
There are some things you need to know about your privacy online - the Electronic Frontier Foundation has published a guide to surveillance self defense that you should read if you are concerned about your privacy online because, while your practitioner is not actively watching you (there is no financial incentive for your doc to spend hours poring over your online activity) what you do online is not private and you can reasonably expect that anything you've posted to Reddit or any other public forum may be associated with your real-life identity if you do not take precautions.
The threat to your privacy here is not any one person (if you have suspicions about the motives or intentions of a person and you can't conclusively explain why watching you would be financially-rewarding for that person and provide evidence to support your theory, you're most-likely making connections that don't exist) but, rather, the systems (governmental, societal, financial) that govern how our society operates.
In China people are already being surveilled by their government to establish a "citizen score" that factors in everything they do or say online to determine whether or not they can exercise "rights" (in China these are actually "privileges") like freely travelling around the country or getting loans, etc.
Could something similar happen in the United States? I believe it's already happening just in terms of the advertising that individuals are displayed (ever notice how something you searched for ends up appearing in ads across sites you visit? The practice is called "remarketing" and it reveals the extent to which advertisers are surveilling and interested in your online behavior).
So... all things considered:
Does anyone else think it's possible that our psychiatrists/therapists are on Reddit?
Yes but they have no incentive to look for you.
And that they know our usernames and follow us?
No your therapist doesn't have the resources to connect your username, email, and IP address to your real-life identity... but yes, there are entities out there who do have that capability and yes they could follow you around, if they cared about you (but, instead, they have computer programs sifting through all your data and storing things that may be interesting to them later).
Watching every post we make to use as research?
No nobody is getting paid to study you.
Much as it hurts my own ego to say it (paranoia = the ultimate panacea for feeling like nobody cares about your life) people with psychiatric difficulties are only studied extensively in clinical environments and we're common enough that nobody's going to spend money to fund research outside clinical environments.
I did go on a blind date once with a psychology grad student who was studying blogs she'd identified as run by people with psychotic disorders (she was really interested in how they used different tone/voice/fonts to express themselves and had some kind of thesis she was working on) which was actually really funny, as I was running a blog that did exactly what she was describing (it's at archive.org) - but that's the extent to which our online activity gets any personal attention, curious people w/o the ability to "connect the dots" even if they wanted to.