Synthroid like any drug can have side effects. But the real answer here is, if your synthroid is not given in the proper dosage your underlying thyroid problem will still be there and that can cause panic attacks and all the other symptoms you mention. Many people who are told they have an anxiety problem actually have a thyroid problem, but if the Synthroid is adjusted properly it should eliminate this problem. Trouble is, it has to be readjusted regularly and sometimes it's very hard to get it just right, and once you're on Synthroid, your thyroid stops working altogether and your only option is the Synthroid. So if you started getting these symptoms only after you started Synthroid it might be it's not adjusted properly. You need to see your endocrinologist to determine this.
Best thing to do is to call the doctor that prescribed it. Talk to them about it. But hopefully you are working on the anxiety overall . good luck
Not directly causing panic, but if you have any of these side effects you might get anxious. You can see some of your list is a potential side effect of synthroid but not many people get side effects so your list could be just in your head. For instance, it takes careful observation to determine if the med causes loss of appetite, or if any of many other possibilities cause it. You need to discuss with your doctor if you feel side effects.
https://www.synthroid.com/what-is-synthroid/side-effects