J.,
I am not prone to run to a doctor at the first sign of symptoms for me or my family, nor do I run to the vet with my pets for things that appear to be treatable. However, with your description, I encourage you to take your dog to the vet. Inactivity does not sound like an expression of anger to me, especially when it is coupled with a "throat noise." Perhaps he swallowed something that is hung in his air passage. IF the cough is indicative of something wrong that gets progressively worse, this could have outcomes that you would not want: such as the condition becoming untreatable and/or it might cost you MORE to treat the longer you wait. If he does not improve, you will regret NOT getting treatment.
Actually, the kennel may or may not have anything to do with the condition - and until you know what the condition is, it would be hard to tell (e.g. he might have swallowed something from your home or car just prior to going in to the kennel).
You also mention having left your "dogs" (plural.) Do the other dogs left at the kennel exhibit any symptoms? Also, have you spoken to the caregivers at the kennel to see if they (a) noticed any problems/symptoms when caring for your beagle, or (b) if they are have had an outbreak of any illness, like kennel cough?
Even though you are busy, I think it would be good to get your beagle in to the vet ASAP. Our pets are dependent upon us for care, as are our children. Like infants, they cannot tell us what they are feeling.
God bless you and your busy life - and best wishes on your beagle's health,
K.
P.S. - Perhaps the following is a scripture will make you smile. It specifically talks about how God feels about His creation and indicates how much He loves animals (CAPS added for emphasis):
Genesis 9:8-17 - Then God spoke to Noah and to his sons with him, saying, "Now behold, I Myself do establish My covenant with you, and with your descendants after you; and with EVERY LIVING CREATURE that is with you, the birds, the cattle, and EVERY BEAST of the earth with you; of all that comes out of the ark, even EVERY BEAST of the earth. "I establish My covenant with you; and ALL FLESH... God said, "This is the sign of the covenant which I am making between Me and you and EVERY LIVING CREATURE that is with you, for all successive generations; I set My bow in the cloud, and it shall be for a sign of a covenant between Me and THE EARTH. "It shall come about, when I bring a cloud over the earth, that the bow will be seen in the cloud, and I will remember My covenant, which is between Me and you and EVERY LIVING CREATURE of ALL FLESH; and never again shall the water become a flood to destroy ALL FLESH. "When the bow is in the cloud, then I will look upon it, to remember the everlasting covenant between God and EVERY LIVING CREATURE of ALL FLESH that is on the earth. "And God said to Noah, "This is the sign of the covenant which I have established between Me and ALL FLESH that is on the earth."
:) And regarding a regenerated earth and animals in heaven? Just my view, but I don't think God makes a covenant with "dust!"