Getting your blood tested every 2-3 weeks at first and then every 6-8 weeks sounds like a reasonable schedule when you’re experimenting with allopurinol dosage. Guidelines will say stuff like “every few weeks”. How often really depends on individual factors but waiting 3 months for your first blood test after initiating allopurinol is clearly irresponsible.
For one thing, you need to get your liver and kidney function tested. It doesn’t take 3 months to damage your liver and it’s not painful. You might not notice anything until it’s too late but a blood test should show anomalous values if your liver didn’t take well to allopurinol.
You can in principle start with less than 100mg actually. Allo pills are often designed to be cut in half. I’m obviously not saying you should lower your dose, only commenting on the “minimum dosage”.
It’s not recommended for a gout sufferer to lose weight so fast. Anecdotally, people often seem to get gout on low-carb diets.
There’s way too much noise in test results to draw any conclusions about the effects of diet based on only two tests.
I’m not sure you had “gout hell”. Your test results were a bit high for that. Attacks can become more frequent and spread to other joints after a while anyway. That’s one of the reasons gout shouldn’t be allowed to fester several years without treatment.