You can certainly hire your own appraiser if you're that concerned. Keep in mind that the lender was concerned only with determining whether their loan to you would be adequately secured--if the report they received satisfies them, they're not going to ask any further questions of the current appraiser. Hiring your own appraiser will cost you $300-$500 and usual turn time is a week or so.
Contact a 'busy' agent in your area and ask them to prepare a market analysis for you. A 'busy' agent will be familiar with your area and competent to provide you with an accurate estimate.