Running a network capture on my computer and filtering for DNS gives me these results:
Going to a web site, www.hp.com in my test, initiates 2 A record lookups from my computer for www.hp.com and several more lookups for additional FQDN "resources", such as welcome.hp-ww.com and met1.hp.com so it seems perfectly normal that DNS queries will outpace actual site visitors.
Increasing the TTL value is likely to help only for people that make frequent visits to your site. It has no bearing on visitors whos' DNS resolver caches don't have your DNS records already cached. Every visit from someone who hasn't been to your site within the TTL period will require a new DNS lookup. Also, even with a 3 day TTL, if someone who's visited your site has rebooted their computer or flushed their DNS cache in that 3 day period will likely require a new lookup to find your DNS records (dependent on their own DNS infrastructure).
My suggestion would be to run a network capture on your computer (flush your DNS cache first) and start a capture, filtering for DNS, and then visit your site. Stop the capture and take a look at it to see what DNS queries are issued from your machine. This will give you a good idea of the DNS queries being issued, the answers being returned, and may point out some misconfiguration in your DNS that you're unaware of.