We live in South Texas and it gets extremely hot in the summer. We sealed up the ceiling in the closet where our furnace is because the heat from the attic was so extreme you could feel the heat when you walked past the closet. The return air is right below the closet door where the furnace is and the a/c was constantly running due to the hot air coming from the attic was being returned. We completely sealed the door. Is that all we should have done? It seems ever since we put that ceiling in, the a/c unit seems to be running more rough. I guess my essential question is: Is that open space above the furnace required or can it be sealed up so that heat from the attic is blocked?

Do you not have any vents in your roof to release hot air from your attic ?

We live in South Texas and it gets extremely hot in the summer. We sealed up the ceiling in the closet where our furnace is because the heat from the attic was so extreme you could feel the heat when you walked past the closet. The return air is right below the closet door where the furnace is and the a/c was constantly running due to the hot air coming from the attic was being returned. We completely sealed the door. Is that all we should have done? It seems ever since we put that ceiling in, the a/c unit seems to be running more rough. I guess my essential question is: Is that open space above the furnace required or can it be sealed up so that heat from the attic is blocked?
Yes, the roof has several vents

You need to either track down an installation manual for your furnace or have a technician look over the installation. There are minimum clearance distances. In heating mode, the furnace requires combustion air.

Agree labman.. make up air for combustion is extremely important. Lack of air for combustion can lead to a bad running furance all the way to flame rollout and carbon monoxide production. Please find the manual and check clearances and venting instructions.