According to the Standard Methods: The alkalinity measured value may vary significantly with the end-point pH used. Alkalinity is a measure of an aggregate property of water and can be interpreted in terms of specific substances only when the chemical composition of the sample is known. Hydroxyl ions present in a sample as a result of dissociation or hydrolysis of solutes react with additions of standard acid. Alkalinity thus depends on the end-point pH used.

For the determination of the alkalinity related to the bicarbonate equilibrium we use 4.2-4.3 as pH set point.

You have a complete explanation of the procedure in the method 2320.

http://folk.uio.no/rvogt/KJM_MEF_4010/Alkalinity.pdf

Thanks Nicolas for the explanation and reference. But I am just wondering is it valid to only use a pH meter and the acid to measure the alkalinity. Then record the endpoint of pH 4.5.

Based on the SOP that you provided, they use potentiometric and titration methods. I probably used the titration method (I am not sure, I hope you could clarify the method I'm using), the only difference was instead of using burette, I used syringe to dispense the acid.

Here's the link to how I did my total alkalinity measurement. 

http://www.wetnewf.org/pdfs/measuring-alkalinity.html

Can this method be used? I did not use any indicator, just a pH meter and acid.

The pH meter is more accurated, probably better than an indicator. And the use of a syringe maybe is less precise than the burette, but is a way of measure the amount of added acid, so, I think the method you are using is right (a titration, a known concentration and volume of titrant reacts with a solution of analyte or titrand to determine concentration).