You should start by calling the clinic and asking them to tell you how the visit was coded. Some clinics have different billing codes based on the complexity of the visit. If you have one thing you are seeing the doctor about, that could be coded differently than if you have 4 things you are seeing the doctor about. In fact, even if you are there just for one ailment, but while you are there you happen to ask a few quick questions about other possible ailments, the doctor could decide to use the billing code for the higher complexity.
If when speaking to the billing department it is determined that the visit is using a higher complexity billing code (and a higher charge as a result), you could then request that it be re-coded with the lower complexity visit. Realize if you request that they will probably have to first get approval from the doctor that saw you.
Note: I am basing this answer on first hand experience about 6 months ago in Illinois, where the situation I described happened to me because I asked some unrelated questions about other possible ailments at the end of a visit to an after hours clinic. The billing department explained that my visit was coded for 4 issues. (3 of them were quick questions I asked about at the end of the visit, one of which she referred me to another doctor. My additional questions probably extended the visit by 3-4 minutes.) In my case I never got the bill reduced, mainly due to my own laziness and my knowing that I would hit my deductible anyway this year. Of course I can't say for sure if this is what happened in your case, or even if this practice is widespread. This was the first and only time in my life that I encountered it.
As a side note, your primary doctor would likely rarely ever bill you for a more complex visit, as it likely wouldn't lead to much repeat business.
As for your last question regarding your credit: if the provider decides to lower the price, and you pay the lower price, this in no way can affect your credit.
Surprising Update: When I called the billing office months ago, I had asked if they could confirm the code with the doctor, and I was told they would look into it. I never heard back, never followed up, and assumed that was the end of it. Well, today I got a call back (months later) and was informed that they had re-coded the visit which will result in a lower charge! It's still pending the insurance adjustment but at some point in the future I expect to receive either a credit on my next statement or a check in the mail. (The price difference pre-insurance in my case has gone from $359 to $235.)
Update: I did receive a check for the difference. The check was dated July 20, 2016, which is just over 2 months after the phone call informing me I would receive it.