It does work, but it's not really a panacea. It's more something you have to do every day a few times a day. There's a physiological basis for it, your heart rests on your diaphragm and it slows down with slow, purposeful breathing. Your heart slowing helps your nervous system stop firing as fast which helps with anxiety. It's something to do and to focus on when a person is in full panic attack but it's not exactly Ativan if you get my meaning. It's more a thing that helps the longer and more you do it.

A lot of skills and exercises we do for the first few times feel uncomfortable, so a little discomfort is to be expected. If you're being told to do this as a way to help with anxiety, don't worry the discomfort is a part of the process. Feeling like your breathing is off is a very, very common anxiety symptom. You already got it checked out by a doc, right? Sounds like your breathing and lungs are okay from a medical and physical point of view. Feeling like the air coming out is too irregular is interesting, cause you should have full control over the rate - unless you mean the very very end of the breath, cause then yeah it gets raggedy at the end if you're blowing everything out. That's normal, everyone is like it - but whats not normal is being told to blow all the way out to the very ragged end, you shouldnt have to (this is supposed to be relaxing lol). The discomfort in your throat and chest with deep breathing is also unusual, but you said a doctor already cleared you so likely you just need practice and it'll come more naturally and easily with time.

Keep an eye on how your breathing feels, if this is still an issue with you the next couple weeks I'd bring it up with your doctor again. Also, it's stethoscope lol. That just lets them hear your lungs, they're listening for wheezing, crackles, and if air entry is getting all the way down to the bottom of your lungs. There's other tests for lung function like a Pulmonary Function Test, methacholine test, xrays etc etc - but if they listened to your chest and said you sound good and you feel like you're getting enough air most of them time and maybe they even did a lil SpO2 test on your finger, that should be all the check up and test you need.