My dachshund is 16 yrs. Old. He is drinking a lot of water but only after being sick.

I'm sorry but your dog is reaching the end of his ability to digest food and you need to prepare for the end of his life. He's too old for a lot of treatments and surgery, and what can be done will be expensive and only prolong life a little. Talk to the vet or staff at the vet about this, find ways to make him comfortable and warm, and think of soft bland foods he might be able to tolerate, and consider putting him down soon. Basically give him whatever he wants. He's going to want to be near you at all times.

Take into account his well-being otherwise, appetite, activity, his ability to get around, his attitude. Any vomiting etc. He is a little up there in age, but small dogs tend to have longer life spans, especially if he has led a healthy life thus far. A visit to the vet to see if he has developed any health problems that can be easily dealt with would be in his interest.
Also if he is really gulping down the water and filling his little stomach to full it could attribute to the vomiting.