Need help with Twitter search

I started a new twitter account 2 months ago and noticed that my tweets with links never show up in the twitter search. But tweets without links show up with no issues.

My question is how do you get your account to show up in twitter search? I started a new account as a test and my first 2 tweets without links showed up. But then I gave a link tweet and the same issue came up.

Have others seen this to their account and what needs to be done to overcome this? Thanks.

Has nobody had this problem yet? Any advice would be great to fix the situation.