No! Don't start a new campaign! You are just at the point where the game get's interesting.
By having conquered so much land already you should have enough money to build quite an army. So don't buy too many weak local armies, but concentrate on roman legions. For example phalangite mercenaries, cretan archers and gallic riders are good support, but don't waste your money on Lugoae or other light militia reserves.
Send about 2 fullstacks against gaul and against hispania each, try to make a beachhead in Africa with one or two fullstacks and try to secure your border in the east with one or two. Build city walls to help in the defense of your eastern cities. If you can establish a beachhead in africa, you will force the karthagians to turn around and stop investing in iberia.
I know you can't recruit roman troops outside italy - so produce reserves, transport them to the frontlines with ships, and reinforce your troops by merging them. You don't have to return your frontline troops back home to reinforce them. It's a question of logistics.
The turns will take a bit longer, but you will wade through rivers of blood and in the end you will triumph. I hope you will enjoy it. It's a hard time you have to go through, but it is the most interesting part of the game: for the first (and last time) your empires supremacy is in question, cause all enemies unite against you. Break your enemys backs this time, and they will not be able to threaten you again.
Good Luck!