If the accounts you have added to the Chart of Accounts are either income or expense accounts, they should automatically show up in the budget if you create a new budget. Otherwise they will not show in the budget.
Could you confirm if your new accounts are under the Income, Other Income, Cost of Sales, Expense or Other Expense Account Type?
Currently there isn't a way to edit the budget accounts after creating it. However, the expense sub-accounts should also display in the budget - if you create a new budget or copy the budget, do the new accounts show there as well?