Lately I've been having troubles with my mySQL databases. I include the page on all of my pages using the require() function to connect to my database. Lately though, whenever I go to my site, it gives me errors like this:

Warning: MySQL Connection Failed: Too many connections in /home/super/public_html/connectinc.php3 on line 2

Since all of my content is in mySQL, these errors make my site useless, so I need to get the problem fixed as soon as possible. Are these problems likely my host's fault, or am I just getting too many visitors for my site to handle?(I get about 1,300 uniques per day and about 20,000 page views per day)