There is no reciprocal agreements between Arkansas and Oklahoma.
If you are a resident of Oklahoma and worked in Arkansas as non-resident - only income from Arkansas sources would be taxable for that state.
On your Oklahoma tax return - which you will file as a resident - you will claim a credit for taxes paid to another state (Arkansas in your situation).
Because you had a loss from your self-employment activities - that losses will reduce your taxable income.
You may claim a deduction for unreimbursed employee business expenses using Form 2106 or Form 2106-EZ and on Form 1040, Schedule A .
Travel expenses paid or incurred in connection with a temporary work assignment away from home are deductible. However, travel expenses paid in connection with an indefinite work assignment are not deductible. Any work assignment in excess of one year is considered indefinite. Also, you may not deduct travel expenses at a work location if it is realistically expected that you will work there for more than one year, whether or not you actually work there that long. If you realistically expect to work at a temporary location for less than one year, and the expectation changes so that at some point you realistically expect to work there for more than one year, travel expenses become nondeductible when your expectation changes.
For more information on travel expenses, refer to Publication 463, Travel, Entertainment, Gift and Car Expenses.
Let me know if you need any help with reporting.