Thanks for relaying the info about your son, particularly that he does not have psychotic symptoms and that he recently broke up with his longtime girlfriend. I think that is a key factor to his distress. When people are depressed they often do not appear down but more anhedonic (lacking pleasure or interest from activities they once enjoyed). They often isolate themselves and may have difficulty with attention and concentration, which can lead to difficulties/being reprimanded at work (possibly hence feeling paranoid at returning to work). This is a vicious cycle as it leads to greater self-loating and distress, depressed mood, and avoidance of activities.
It sounds like your son is trying to do things that will make him feel better - going for a swim, seeing a therapist - and that at times he can muster up the energy and motivation for such while at other times it becomes much more difficult.
Since depression is diagnosed as more than 2 weeks of depressed mood/anhedonia plus these other symptoms it would be helpful for him to seek a medication evaluation if these symptoms have persisted for more than two weeks. It has been widely noted that medication plus psychotherapy is more beneficial for clinical depression than either alone. This does not mean that there is anything wrong with your son nor that he will need meds for years if perscribed. What it may mean is that he needs a boost to kick start him back on track. To find a psychiatrist in your area you can ask for a referral from the therapist that he saw or if he has insurance you can call (together if possible) the insurance company and schedule an appointment with someone who is in network. If he chooses not to go to the appointment or to therapy he may feel worse so it is imperative that he attend these appointments just the same as if he had cancer and needed to see an oncologist. To help him increase motivation to go you can use a simple motivational interviewing technique where you put the conflict of going versus not going back in his lap rather than you taking one side (that he should go) and he takes the other side (that he does not want to go). Saying something like, "You tell me that you don't want to go to your appointments and at the same time you say that you feel depressed/anxious/badly." If the therapy appt was helpful to him you can add that he did find it helpful. If he did not find it helpful, prehaps it was not a good fit with that particular therapist because of her age, gender, theoretical orientation, etc. It is important that he take some responsibility for his care since he is an adult, although your help is certainly imperative at this point. Hope that helps. Please let me know if you have any further questions.