Yes! if you’re physically running camps in California, your Illinois entity will usually need to register as a “foreign entity” in California. That means filing with the CA Secretary of State and paying annual franchise taxes/fees.
You don’t necessarily need a new company, but you do need to be compliant in every state where you’re actively doing business. Since each state’s rules differ a bit, it’s smart to double-check with a CPA or attorney so you don’t miss ongoing filing or tax obligations.