I have a conflict on my second semester regarding one of my electivs. It wasn't put on my schedule because it conflicts against my core. I'm a first-year engineering student and the particular elective is Music History.

In case I can't get a last minute suggestion from someone before the re-scheduling opens (which is highly possible...) what should I do tomorrow?

If music history conflicts with something that you need for your degree there's nothing you can do but change it for another elective or wait to take it another year. Required courses trump electives.

Will I get penalized or anything for not completing the total 37 credits I needed to earn for the first year if I take it another year? Also, will it be too late for me to take another electives now?

You have to complete the 37 units in order to move on to year 2. You could take the extra units during the summer but the grade you get will only count towards your cumulative GPA.

You may not get into another elective right now but when the drop/add period comes in September you will get into another elective. There will be a lot of people changing courses during that period so I promise you that you will get another elective.

hmm, alright. so should I just ignore the conflict for tomorrow? (or later today)

Try to fix it if you can on SOLAR before September, if not then yes wait until September. Don't drop the Music class just in case SOLAR does something stupid like tell you that you're not fully registered because you're under the unit count. In Sept you can switch it around for something else.