The only firearm you may possess while archery hunting is a handgun for self defense, not for hunting. See below for the overlap of archery and muzzleloader seasons.
(2) Prohibitions. While hunting deer during the archery deer season, it is unlawful to:
(i) Use or possess a firearm. Exceptions:
(A) A person may possess certain firearms during the archery deer season under the authorizations of section 2525 of the act (relating to possession of firearm for protection of self or others).
(B) A person may possess and use both a bow or crossbow and a muzzleloading firearm during the overlaps of the early archery and muzzleloader deer seasons and the late archery and flintlock muzzleloading deer seasons if that person is in possession of both a valid archery deer license and a valid muzzleloader deer license and meets the greater protective material requirements for the muzzleloader deer season, if applicable.
When you are up to your butt in alligators, it is hard to remember your intent was to drain the swamp. Stay focused!