Do you know what you want to do once you're done with school? It sounds like architecture but perhaps you're not sure. 

My background is similar--a BS in Engineering, though a few classes short of the accredited BSCE because it was also most of an art/arch history degree. I was also on the concrete canoe team two years, and we made it to nationals both times! 

Most of my classmates went on to grad school for either architecture or engineering. I decided to build furniture and later houses, but I wouldn't recommend that path if you know you want to be an architect (though a little on-site work is good training for any architect). 

Many of my classmates went to Rice University to get a master's in architecture, or some version--I'm not a geek about degree paths. I believe they had only an informal relationship with my school, but--25 years ago, anyway--they were definitely ok with admitting engineering-oriented students. I recall my classmates scrambling to get portfolios together, since our program was light on studio work. I bet plenty of graduate programs would be happy to admit students like you, and you don't have to be the most creative person in the world, but you would need some sort of portfolio of work.  

What I meant by sharing the information above is if my extracurricular activities are of any relevance when applying for the M.Arch I? I did finish design II. I went to an arts and design high school, and did my freshman year at an art school. I don't know if my skill level will be enough to apply to a Master's program in architecture.

And does having a Master in Structures carry any value in architecture school or in practice when you become an architect, or will I be taking it too far and my undergrad elective courses will be covering my bases?

Thank you so much for those that have replied thus far and may this be of help to someone that is in a similar position.

And to clarify, yes, I intent in becoming an architect. 

Please recommend schools that offer funding to students like me, and/or firms to intern at, portfolio suggestions. Anything that would help this dream come true. 

I used some paid online courses after graduation for up my skill

It doesn’t matter your previous degree, extracurriculars of actual substance always help. You’d be surprised how few engineering majors end up applying to arch programs, compared to those with mostly social sciences/humanities/art backgrounds. If anything being in that minority of candidates will help set you apart. I know someone who did structural undergrad, then arch grad, then structural grad. Ended up just working as an engineer. If you choose to work as an architect the master in structural is overkill, you already have an undergrad which is light years more structural understanding than the average architect. You can always work a while, which I would highly suggest, and then decide if you want to go back and do more schooling. Real world experience is completely different than school. You may find you prefer the day to day in an engineers office over architecture, or perhaps dislike both. Better to figure that out now than after 3 degrees. In regards to funding, if you have a solid application and the school really wants you to attend, most schools of a decent ranking tend to have some amount of merit based scholarships available. Again your previous major is irrelevant to obtaining funding, what counts is the general strength of your application / candidacy. It’s not common but it’s not impossible to get a full ride to even the most expensive of schools. Keep in mind however, even if tuition is covered you must consideration cost of living in the location and that you will be earning little to nothing during that time as grad school is very much a full time endeavor, especially if you want to set yourself up well for post grad. Choose your schools based on where you want to make lifelong connections / live post grad, what the type of work is and if it’s something you’re interested and excited to pursue, and then focus on putting together a stellar portfolio / application to get that funding. Pick a few back up schools that are uber cheap in case your application isn’t all that stellar and decide if the cost is worth it. You can always work for a while and reapply if it doesn’t go well the first time.

can agree with you

This is an interesting discussion. 

I only have a Bachelors or Architecture.  It was a five year, selective admissions program and with the exception of your first semester it was crammed with architectural classes (roughly 75% of your course work).  Studio started at the beginning of your second year and continued throughout the program.  Upon graduation I felt I barely had enough knowledge to function in a firm even with working part time and summers for three years.   

I'm a bit surprised by the number of students with no previous schooling in architecture that are accepted into a schools masters program for architecture.  That must be some masters program to cram all that coursework into two years!