How to protect my mounted insect specimens from ... insects?
I ran into the same issue when collecting bees in a hot, humid environment.  As arboviralstated, freezing is a great way to help with the infection but keep in mind:


It may not kill all of your pests
It will not keep your specimen from future pests
It may damage your samples


From the USDA website, you could pretty cheaply use paradichlorobenzene or naphthalene:


  Two of the most widely used fumigants are paradichlorobenzene (PDB)
  and naphthalene, both of which are obtainable in balls or flakes.
  Never mix PDB with naphthalene as they react chemically and produce a
  liquid that may damage the collection. It should be noted, that most
  major collections are now moving away from the use of solid fumigants
  because of health concerns and in some jurisdictions, it is now
  against regulations to use some fumigants.


That being said, I used a combination of freezing and then naphthalene (moth balls).  It's cheap and anecdotally pretty effective for my purposes.  I also didn't access my collection frequently once established, so the health concerns were less of a worry for me.  

Definitely worth mentioning that there has been talk that using naphthalene  or PDB may damage DNA and hurt DNA extractions on down the road, but this is demonstrably false.  That being said, keep in mind these chemicals still pose some heath effects - especially with prolonged or occupational exposure - such as poisoning and carcinogenic risk.