Hello from JustAnswer.
Yes, it would be appropriate to check thyroid blood tests. Many symptoms of thyroid disease are non-specific, particularly, so it is appropriate to check thyroid tests in someone with a wide variety of symptoms. There even are some national guidelines that recommend thyroid testing in people without symptoms, because the symptoms can be so insidious that they may be attributed to aging, although there is no consensus of the exact age at which to start testing or the frequency of testing. However, in your case, with various symptoms, it would be appropriate to check thyroid tests.
If I can provide any clarification, please let me know.