People who like the French are Francophiles.
People who like the English are Anglophiles.
People who like the Chinese are Sinophiles.
Is there a related term for people (like me) that like Americans?
No-one’s ever had the need to invent a word for someone who likes America - 'cos they don’t exist 
There’s no direct equivalent, except the slang word - ‘yankophile’, but ‘Americanist’ can have pretty much the equivalent meaning as the above examples.