I am sorry to hear that you have been told that you have a sinus infection, and that now your throat feels like it is closing down and it is hard to swallow. I am not sure exactly what is going on by the constellation of symptoms that you have given me, but I am happy to give you some information and point you towards what I think is the right direction to help sort out what might be going on. I don't know what type of physician you have seen so far, but I am going to recommend that you make an appointment with an otolaryngologist
or ENT (Ear Nose Throat) physician to get evaluated. They will be able to examine you, and perform an in office scope exam to examine your sinuses and throat to help determine what is going on. You ask if it is normal to feel like it is hard to swallow and that your throat is closing with a sinus infection, and the short answer is that it is not normal. We see people in the ENT clinic all the time with sinusitis, and this is not a common complaint. I can also tell you that a lot of people show up to the ENT clinic with 'sinus headaches' that when they are full worked up and properly diagnosed, don't actually have sinusitis. These are some of the reasons that I think it would be beneficial for you to see an ENT. Best of luck.