I have taken probably five different free IQ tests over the past year and gotten scores ranging from 118 to 147 depending on which one I used. That range alone tells me none of them are measuring anything real. I genuinely want to know my actual cognitive profile but I do not know where to start. What would you actually recommend to someone who is serious about getting a legitimate assessment?
The range you got across those tests is actually a perfect illustration of why free online tests are worthless. A properly designed assessment with real norming should give you scores that are consistent within a few points across retests because it is measuring something stable. Getting a 29 point spread means those tests were not measuring the same thing, or anything reliable at all. For a serious assessment your best options are a clinical evaluation from a licensed psychologist for maximum precision, or a properly normed online battery like RIOT IQ which covers 15 subtests across 6 CHC domains and gives you a real cognitive profile rather than a flattering random number. The score consistency you get from a legitimate test is itself evidence that something real is being measured 
A 29 point spread across different tests is not a confidence interval, it is chaos 
That is not measurement error, that is five different tests making up five different numbers. The first sign of a legitimate test is that your score is stable across retests within a reasonable margin 