You can upload phpmyadmin to your hosting account but it will only work if you have PHP support enabled. phpMyAdmin is just an interface to interact with MySQL. Where your mysql database will be?

@k2k - when you buying web hosting the package says what it contains. These days only very basic and cheapest options do not include database in their offer. If you got one of these, then I have to say that unfortunately you made mistake as buying database server on its own will cost you more as to get hosting with DB included. Try to speak with your hosting provider about possible upgrade of your package, I'm sure they will happy to do for you.

If the package which you have contains DB, then just look up login details from the hosting administrator and get working on your database.

As to your question about installation of phpMyAdmin, this tool is most likely already made available to you ( well I seen it with MySQL database, not sure about MS SQL or Oracle) as it is tool of choice for huge number of hosting companies and you do not need to install it.