Creare boundaries. If the goal is to keep your job, creating any kind of boundaries will need to be done very sensitively and diplomatically. Also, the size of the business, and whether there is an Human Resource department matters, that can ultimately protect you from bullying.
Personally, unless absolutely necessary (due to needing leave from work due PTSD exacerbation) I would not reveal to anyone else, at your work, anything about your condition,especially within the first 90 days, where many businesses have a trial period for employees. After this time, if you work enough hours per week, you can submit an FMLA for PTSD that will allow you to not have any PTSD related sick time counted against you.
Secondly, to decrease people taking to you about PTSD, now that you have opened the topic, you will need coping skills to gracefully deflect and signal to them that you are now wanting to talk about other things, and make sure you do not appear hostile. To support ethical treatment of everyone at the workplace, you can set an example of not "making fun" in the work place. Laughter is good, when it is not mocking others.
Acts of kindness, are helpful ways to mix in with others.
If problems like bullying develop, you may need to ask HR or your manager for help. However, from the limited information I have, it soundslike the manager and supervisor are not mature, nor trustworthy. For this reason, you may want to see if you can create boundaries yourself at work. And save PTSD talk for you friend at outside work.