You may be able to contribute additionally to an IRA. If you are covered at work by a qualified retirement program (such as a 403b), it still may be possible to contribute to another IRA within certain income limits. Please see the following FAQ on this: https://ttlc.intuit.com/replies/3301534
Depending on where your income range is, therefore, you may be able to receive additional deductions to your taxable income by making this contribution, which you may do up until April 17 (the filing deadline) and have it count towards the 2017 tax year.
You cannot open your own 403(b) plan because that is an employer funded account only. However, depending on the plan administrator's policy at work, it may be possible to have more income sent to your 403b designated as a 2017 contribution if allowed. But you cannot open up a new account on your own.