Hi J.,
Quit beating yourself up!!! Keeping kids healthy is not something we alone have control of. There are some tidbits of info that could be helpful that I will share.
First, I am amazed at how easily drs give vaccines to kids today that are not 100% healthy. When my oldest (and she is the only one that received vaccines) got hers, if she even had a bit of a sniffle, they would not give them. They said it was important their immunity systems were strong. The vaccines can and do impact the immunity system...as the vaccines are injections of the diseases so that the system will fight it. The more subjected to things the harder the system has to work. Sometimes it might be more than the system can handle, and the person becomes ill. Thus this could be what happened to your son.
Teething is yet another "stress" to the body. Each stress has the potential of weakening the body and its immune system. This is why we often see babies with runny noses or loose stools when they are teething.
The probiotics are one of the best things you could do! Keep giving them.
Yes, he could be getting sick. Basically, his system may be out of balance. How to bring it into balance? Rest, probiotics, highly nutritious food, love and attention! Polarity, cranial sacral therapy or even chiropractic could help restore his system to balance. You can also lightly massage his body, esp his feet.
I would keep any highly allergenic foods from him until his body is stronger again. No sugar or processed foods either. Don't worry about his appetite, his body needs to focus on healing, not digestion. Babies will generally start eating when it is healthy for them to do so. Make sure he gets enough fluids, tho. Cook some veggies to make a broth for him, offer him sips often. Cooking carrots and celery, straining, and drinking the broth is good to replace the electrolytes. Nettles tea is highly nutritive, too, and would be a good choice. Chamomile tea would be good for his digestive system. Even just sips can help, if he wont easily drink it.
Each child is different, as you know, and how each reacts to stressors in their lives is different. Some people are born with strong immune systems, while others' are easily compromised. If we had it all figured out, there wouldnt be any sick people! :) There are ways to help strengthen the immune systems, some of which I mentioned above. Herbs are also helpful. For example, Astragalus can be an easy way to bolster the whole families' systems by adding it to stew, soups, casseroles, or other foods that cook for a period of time. Remove it before serving. This is best used when we are NOT sick, however. There are other herbs appropriate for bolstering the immune system when we are already sick. Echinacea is one. Seek an herbalist if you are not knowledgeable about what or how to use them.
No one likes to see their child sick. Hang in there and keep watching him like you are. If he gets sicker or is sick too long, seek further help. I hope some of these suggestions are useful. Blessings to you.