You have a common misunderstanding of how Viagra works. It basically
functions through relaxing blood vessels. It does not work by affecting
hormones. If any increase in libido occurs, it is psychological, not
directly drug-induced.

So, yes there are drugs that work inversely to Viagra, in that they
constrict blood vessels. This is not what you are seeking.

Yes, there are drugs that inhibit testosterone completely (chemical
castration). They are generally reserved for treatment of certain cancers
such as prostate cancer. With many of them, testosterone levels initially
increase, but with continued use, levels will fall to those found in
surgical castration. There are also drugs that block the receptor
sites for testosterone without directly interfering with testosterone
production. They all come with a long list of potential side effects, as
with any drug that has such a significant effect on hormones.

Talk to your doctor.