Well, you don't have to panic in any situation. What you have to do instead is take a deep breath and clear your head so you can plan what you will do. In the case of a removal, the focus really is on the packing and the transportation of your things. Nevertheless there are also some more tasks such as informing utility companies, subscriptions and banks. You have to list everything down so you will not forget anything. The process will be smoother for you too.
 
You could start by sorting your things and listing down everything you will bring to your new home. Then segregate the things you will not use anymore so you can dispose them. You can hold a garage sale for this. You can also auction them off in eBay. You can, of course, give some of your stuff away too. While selling them will raise money, donating them will also lessen your expenses in packing and transportation.
 
Before you start packing, buy enough packing materials. Your list would help you estimate how many boxes, packing tape, bubble wrap and other materials you will. You could also opt to hire the removals company to pack for you if you don't have the time to do it yourself. Just make sure that you look for a reputable company to do it and to transport your things to your new home. With fewer tasks at hand, you would have more time for other things so you will feel less panicky.