If your application is being blocked due to exceeding the limit, then you should get a 400 HTTP response code. If you've written your application such that it generates a blank page when it gets an HTTP failure, then you have your answer. (How you check for HTTP errors in your particular development framework is a separate matter.)
You should use the API instead of scraping the public Twitter pages because IP addresses are subject to API rate limiting just like authenticated API accounts. When you authenticate with your account, you're not subject to the IP limit, so other people abusing Twitter from the same IP address (as might happen from a shared server environment like Google's) won't limit your use. This is all explained in the Rate limiting documentation from Twitter.