My initial response is it is a virus infection with asthma and nothing to do with the tirz, but
I just had a second look at your post where it says it goes away if you stop it. If this is true then it is reasonable evidence of a reaction to the drug. How many times has this happened? That type of drug reaction , if that is what it is, is a serious medical issue, if it is causing asthma symptoms, headache and swollen lymph nodes it is a systemic immune reaction and potentially very dangerous. Have you taken tirzepatide from a different source? Did it cause problems? I think in that case, if it has gone away when stopped and recurred when restarted, the medical assessment becomes essential, though specialists in more serious drug reactions are not very common. But at an absolute minimum you need baseline bloods to see immune state and urine checked to make sure it is not affecting kidneys, chest xray and to stop the tirzepatide. I do not think continuing to take it at this point is an acceptable risk. And I do not think trying it again unless under medical supervision is a good idea.
It is not impossible it is due to a contaminant in the tirzepatide, but it is much more likely to be due to the drug. Some type of immune reaction is common , about 5% get localised injection site reactions, and more obscure immune reactions have been reported.