What Are The Side Effects Of Stopping Atenolol While Having High BP?

I am 56 yrs old and I was prescribed atenolol and amlodopine for high blood pressure about 10 yrs ago, shortly afterwards I was also given bendroflumethiazide as my ankles became swollen with use of the medication. I recently visited my dr because I have episodes of giddiness when I get up inthe morning THis has been happening for Two months,somedays are worse than others. His suggestion is that it may be due to the blood pressure medication and said that as long as I have no heart pains or breathing problems then I can immediately stop the atenolol. I have heard scare storiesabout stopping this drug all at once.I am to check my blood pressure each day and if it rises significantly then I am to see him immediately.How do you feel about this