Dogwood anthracnose has devestated cornus florida trees throughout their range. I can't tell from the picture if this is what your tree has, but the dead branch is pretty symptomatic. Once this infection takes hold, there is very little that can be done for the tree. Your County Extension Service would be your best source for a definitive diagnosis.

There are dozens of species of dogwoods, most of which flower. It's unclear to me from the pictures whether your tree is cornus kousa (Asian dogwood) or cornus florida (American dogwood). The leaves and tree form are more kousa-like, but "flowering dogwood" usually refers to c. florida. Not knowing the actual species of tree makes everything much harder.

I don't actually know if it a kousa dogwood. It gets white flowers with rounded petals.

I called the extension office and they had me leave a message on the Master Gardener hotline. I emailed them too.

If it is anthracnose, will I basically just wait for it to die?

The American (native) dogwood (Cornus florida) flowers earlier and before it leafs out. The 'Appalachian Spring' cultivar is supposed to be anthrachnose resistant. I just planted four of those and am keeping my fingers crossed. The Kousa flowers later and after it leafs out. Our town/city (Alexandria, VA) has a city arborist. You could check to see if your town does and maybe he/she could come look. My first thought when I saw your pictures was that yours is a Cornus florida, but I could be wrong.

The extension office emailed back saying it looks like anthracnose, and included a general data sheet on it (see below).

Can I still spray it with fungicide at this point? Right no wit has finally turned summery here (in the 90s this week, no rain). Which fungicide of the three mentioned, if I do?

Here is a link that might be useful: Dogwood anthracnose

The information on the data sheet is first rate and I think any of the three fungicides listed are pretty much equal. Be sure to follow the label instructions no matter which one you choose. It's a little late in the year for application, but check and see what the labels say. Promoting vigor through watering and mulching, avoiding high nitogen fertilizers which promote soft, vulnerable growth, and good sanitation are probably the most important things you can do. The sad truth is, though, once infection takes hold you can slow down the decline toward ultimate death but probably not avoid it long term.