There are two schools of thought.
One says that you match your valediction to the salutation:
Dear Sir/Yours faithfully; Dear Mr X/Yours sincerely.
The other says that you match your sign-off to the content of the letter. In most cases, "Yours sincerely" will do fine, because you sincerely mean what you have written. In some cases, you may be expressing a wish or expectation that the recipient will do something, when "Yours faithfully" might be better.
There are circumstances where there is actually a prescribed form1 but those are very rare.
Without seeing the entire letter it's not really possible to say how professional it is. But in most cases I think people don't even notice and I expect you don't need to worry unduly.
1 If you start your letter with the formal salutation "My Lord Bishop", then it's expected that you end it "I have the honour to remain, Father, your humble and faithful servant". There are other similar formulae for letters which start "Your Grace", "Your Majesty" and the like. But in that sort of ultra-formal communication using the correct form of words is unlikely to be forgotten.