Can my sweat glands no longer work due to radiation therapy?

XRT dose & Whether the sweat producing glands are in the target of the beam could lead to permanent lack of sweating. It does not affect sweat production in any non-irradiated area. Unlike to happen with dose < 50 gy.
That depends on dose. Radiation therapy can permanently shut off sweat glands in the areas of irradiated skin, starting at doses above 30 gy; this can also happen at lower doses if the daily dose is more intense.