Hi welcome to HCM....
Here free t4 should always be done along with TSH estimation....to rule out subclinical
hypothyroidism ....
Second here your cough , enlarged gland and
sore throat should be investigated with......
1.CBC
2.Peripheral smear examination (esp to look atypical lymphocytes )
3.Lymph node palpation.
4.FNAC from swollen gland to rule out its nature
These will help in rule out your diagnosis.
If from above investigation
infectious mononucleosis suspected serological testing done for confirmation....
If bacterial infection there antibiotic given ...
If needed throat swab also taken for culture...
Meanwhile salt water gargles done.
More water...
Benadryl decongestent taken ...
If still cause not clear go through chest
x ray investigation
Advise : consult physician and discuss all these ..
Take care