Yes, I'm afraid you may be right. Yellowing and wilting of the leaves is the first symptom of it. Unfortunately it is really really bad news.
There's not really a cure for it. Usually what they say is bag up the plant to keep the spores from escaping and trash it.
Then don't use the soil they are in for basil ever again (if it is only a small amount of potting soil, you might just want to trash the soil also). The spores can remain in the soil for up to 8 years.
You can start over with new plants and new soil (having bleached the pots first). Green/ sweet basil is the most susceptible. Now that you know you have the the disease around, you would be better off to grow red or purple basil, lemon basil, lime basil, cinnamon basil, etc. Make sure there is plenty of air circulation around them. Don't water the leaves, only the soil. And use fungicides preventatively. The fungicides don't really cure the disease, but they can help prevent it. That would include baking soda solution or hydrogen peroxide.
Here's an article about it: https://vegetablemdonline.ppath.cornell. ... Downy.html