I have a question - why don't you fill out the paperwork manually and send it certified mail? We recommend doing this for changing your repayment plan. You can select PAYE, and you can select you're doing it off-cycle to have an immediate change.
By sending it certified mail, you'll also have confirmed they received it.
This starts giving you a paper trail if they keep making mistakes.
If they fail to change your repayment plan based on that, you need to file a complaint with the ombudsman and move in that direction.
Navient is a Federal loan, which has options such as income-driven repayment. You simply need to apply and you could have a payment as low as $0 if you don't make much money. Forbearance is a terrible option - get on an income-driven repayment plan.
All you have to do is call and ask for this, fill out the paperwork, and you're set (you just need to re-certify your income annually). You can also do it online at StudentLoans.gov.
If you refinance, you lose access to these plans. So while you may save on interest, you likely wouldn't be able to afford your new loan.
It sounds like you're on an income-driven repayment plan - that's why your loan balance is going up, not down. Basically, your payment is set to your income, not to an amount that will eliminate the loan.
The question is, can you afford to pay more?
Second, Federal loans don't have cosigners - so do you have a private loan at Navient, or it is something else (spousal loan, Parent PLUS)?
If it's private, refinancing it can make sense, but you're only going to qualify to do it by yourself if you have great credit.