But there is a war of sorts on within my being at least.
For the flesh lusteth against the Spirit, and the Spirit against the flesh; for these are contrary the one to the other; that ye may not do the things that ye would.gal5.17
You failed to include the whole context about that passage...
Gal 5:16But I say, walk by the Spirit, and you will not carry out the desire of the flesh
17For the flesh sets its desire against the Spirit, and the Spirit against the flesh; for these are in opposition to one another, so that you may not do the things that you please
18But if you are led by the Spirit, you are not under the Law.
19Now the deeds of the flesh are evident
, which are: immorality, impurity, sensuality,
20idolatry, sorcery, enmities, strife, jealousy, outbursts of anger, disputes, dissensions, factions,
21envying, drunkenness, carousing, and things like these
, of which I forewarn you, just as I have forewarned you, that those who practice such things will not inherit the kingdom of God.
22But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness,
23gentleness, self-control; against such things there is no law.
24Now those who belong to Christ Jesus have crucified the flesh with its passions and desires
25If we live by the Spirit, let us also walk by the Spirit.
26Let us not become boastful, challenging one another, envying one another.
In verse 24, it's not talking about human urges (carnality) to eat and sleep and have sex, it's talking about what was spoken of in verses 19-21, which names the deeds of the flesh... letting sin and selfishness taking over. It's not carnality being named in those verses. Aminals are considered carnal so wouldn't that then mean that they would have to deal with those things as well too then? Or did God give humans a special brand of carnality?
When you say that there's a battle going in in your being, you're talking about spiritual warfare there... it's your spirit having a battle between its own selfishness and pride (flesh, not carnality) and the truth of Jesus Christ speaking AGAINST that selfishness and pride.