I'm so sorry to hear you are having these issues.
While some mild lameness or stiffness may be normal if they were lying awkwardly during or after an anaesthetic it should not last longer than a few day and certainly should not be as extreme as you say.
I agree with you, that breathing rate is a real concern and something we need to take very seriously. Anything over 30 breaths per minute sets alarm bells ringing in my mind and warrants urgent investigation.
Similarly, neck swelling is abnormal and would raise concern that she she is not dealing with fluid as she should.
I would first of all want her heart examined. Ideally, she should have a chest xray or heart scan. If we wish to avoid a repeat sedation we could try a conscious xray and should certainly be able to do the heart scan conscious. If we discover she has heart failure (which can cause excessive fluid, breathing difficulties, lethargy etc) we would want to start her on some diuretics (water tablets) and ace inhibitors. This may really help reduce the fluid and ease her breathing.
We would also consider some pain relief to see if this helps with her mobility.
Did she have any blood tests taken AFTER her anaesthetic? It's important we make sure it did not affect her kidney function and we get an up to date idea of how everything is working internally now that she has these new concerning symptoms.
In summary, I think you're right to want to look into things further and there are some diagnostic tests we need to run. We would hope that things will improve dramatically once we have her on the appropriate medicine.