You answered your own question; improve your sleep. Adequate sleep is crucial for optimal immune function, and less than six hours per night is not nearly enough for the vast majority of people. This is especially true for active people who are also doing strength training. Did the sleep issues arise after starting TRT, or did they exist prior? Either way, start with sorting that out. There are lots of good resources out there that can provide tips on improving sleep hygiene. Getting up to around or over seven hours per night will almost certainly lead to improvements in immune function.
Another aspect that may be impacting it, though this is probably less likely, is that your body is reacting to the carrier oil and causing a strain on your immune system due to the reaction. What carrier oil are you currently using? It’d be worth looking into other options to see if it causes improvements. But again, sleep seems like the most likely culprit.
And Guided By Voices also outlined some great additions to your supplement stack to help with immune function, but those won’t address the underlying issue of inadequate sleep.
I’d be hesitant to make dosing adjustments if you aren’t having any other issues. If anything, you could try splitting into 3 doses instead of two to see if that helps with sleep, but again I see no reason to lower dose if there aren’t other concerns… as it is a rather conservative dose and better sleep habits will almost certainly result in improvements to immune function without losing the other benefits you’re seeing from trt.