No, that's a good thing -- maybe. Therapy is hard, and facing things that happened in your life that might have been bothering you for a long time will bother you now. But here's why the maybe -- it's very odd after only 4 sessions for a psychologist to have figured you out, and it's also not necessarily true with anxiety that anything happened to trigger it. True analysis of one's life to discover what is bothering us can take years, especially if it's not something obviously traumatic. By the way, almost nobody doesn't have a some fear of death or separation anxiety, the question is whether somebody gets hyper focused on it to the extent they're too scared to live their lives. With anxiety, most these days believe a form called CBT is the most effective. This form doesn't really care why you got anxiety, it just tries to get you to see how your thinking is interfering with your life, gives you techniques to deal with that, and then sends you out to do things that make you anxious until you overcome it. It's hard, too, and there's never any guarantee that therapy of any form will help anyone -- overall it works about 30% of the time for the one type that you can actually double blind test, and that's CBT, but that doesn't take into consideration that there are a lot of therapists out there and when you find one you can work with, if it works, you're basically cured. Medication also only works 30% of the time, but again, there are so many meds out there to take you might find one that helps, but it never cures the problem -- only changed thinking can do that. I'd keep on with this therapist, knowing any therapy will bother you before it helps you -- you're working right on the sore spot. But if you think this therapist is just being glib or doesn't seem to really be listening but only talking and telling you things you don't feel are true for you or are helping, then you look for another therapist and perhaps another form of therapy.
I think therapy is excellent. Medication and therapy combined work really well and help the vast majority of those who seek it. But in general, therapy riles up a lot of emotions. It forces us to talk about things or look at uncomfortable things. Is it good? Not sure it always is. I am a believer in therapy, don't get me wrong, but if it is creating more issues surrounding anxiety post therapy, then I'd question if that therapist was going down a good path with you. There are good and bad therapists out there. Start tracking in a journal with how you feel. This info will help you decide if you need a new therapist, if this therapy is helping or if you should talk to your GP about the addition of medication. good luck