Can i request immunology labs (t-cell count, iga/g/m) if i suspect weak immune system due to frequent infections? my pcp dismissed them as unjustified

Depends: if you're looking for an immune deficiency, then testing branches out after a simple abnormal blood test. If your type and frequency of infection has a threshold for testing further, then your doctor might justify this expensive testing if indicated, by your overall health and risk. Have a deeper discussion so you both understand each other better, and be sure to explain your fears. Zmd

Immunity: You can, but it may be misguided. "frequent infections" to lay people and to doctors are often two different things. It is not just the frequency but also the type / location and infecting organism that are important in determining whether or not such eval is warranted. Add to this the fact that many "infections" are not infections to begin with and you can see the difficulty.