I suggest you testing for antibodies (TPO) - then you see if you have an autoimmune disease or not... If you do - you MUST take medicine, actually I would take medicine on TSH 8.2 in a heart beat as well. When I was diagnosed my TSH was 9.2, and I did not feel any symptoms... Until I check the list of symptoms and realized that I have many of them. Are you sure you dont have any symptoms? Low sex drive, fatigue, lethargic, low motivation, tired all the time, cold hands and feet, hair falling out, depression, weight gain? These are the biggies. If I were you, I would take the medicine and normalize my numbers. Your TSH should be 1. You will have to check your numbers at least twice a year. Also, consider running a THYROID PANNEL test - not just TSH. Ask for TPO, TSH, T4, T3, FreeT4, FreeT3 and T3 uptake at least! The mucus can be from many things - like dairy... but I think these findings are inconclusive as I eat little dairy if any and I have it too. Good luck to you!
The high white cells are not likely related to thyroid - you may have an upper-respiratory infection with the symptoms you describe.
The high TSH needs to be evaluated. If there are no symptoms, would repeat TSH in 6 weeks to make sure it's not a transient problem. Also, test anti-thyroid antibodies to see if there is evidence of hashimotos -- which would suggest that starting the synthroid is more likely inevitable....
Consider thyroid ultrasound to complete the evaluation -- looking for nodules, inflammation and goiter.