Besides architecture or interior design programs, you can start looking for universities or colleges with a fine arts school that has a concentration or degree in furniture design. If furniture design is your primary goal, that might be the most logical way to go since you get to build furniture in your program and sell it along the way! Some art schools may lump furniture design into an industrial design program, so you will need to do a little digging online.
Architecture will not necessarily be the best place to learn carpentry. You may have the opportunity to build furniture as part of your early projects. but it depends on the program. You could also look into engineering program. Like architects, they are trained to design buildings, but bridges, tunnels, and other structures as well. The focus is structural integrity rather than aesthetics like in architecture. So if you are less artistically inclined, engineering may be for you.
Interior design programs will be far more likely to involve custom furniture building, but again look into programs carefully and see if they focus on your interests. Some interior design programs will get more into remodeling buildings on a structural level like building new walls or knocking them down to make a room bigger.
Another area of study is construction management. This would be supervising construction projects. You would get to learn about how to read blueprints, how things are constructed, working with construction crews, engineers, and architects. This wouldn't be an education in designing things, but actually training you to be the person that gets the building completed.
But if you really want to get your hands dirty in building to figure out if that's what you really like, try to find an apprenticeship program in carpentry where you can talk to real professionals and get advice. They may even have introductory programs where you can observe and help on the job to see if that is what you like. You can also look into volunteering with a non-profit organization that specializes in building houses for people in need. I know Habitat for Humanity has chapters in the Philippines, but I'm sure there are other local organizations that may be through local churches.
I hope that helps! Good luck in figuring things out!