I believe the seven speed equipped bicycles in production for the last decade have all been freewheel bikes.
I concur that you can buy new service replacement 7 speed cassette parts, though.
I concur with Alfeng that you can just change the chainrings (and resite your front derailleur) but sometimes the price of rings makes looking at a crankset pretty attractive. You can change to a hybrid crankset, which would give you higher chainrings. Hybrid cranks usually fit MTB bottom brackets if you get the right kind (there's a few types of spindles.) You could have a 28-38-48 crank. To do this you would need to do some research to get the right parts, a crank puller, the crankset itself, and the willingness to resite your front derailleur higher.
I don't know if you would just be able to get just the big ring for speed and leave the other two, because the derailleur is limited in how big a range it can cover due to the size of the cage. I am not sure you can have a 22 and a 48 ring on the same crank.
You may as well get to a shop and have them tell you what it is because unless you want to buy the socket to remove the freewheel, they'll have to do it for you. Of course, if the freewheel is old and you're going to pitch it out, it's possible to remove at home if you have basic tools and installing the new one requires no tools because it screws on by hand and tightens by you pedaling the bike.