I want to ask for some sort of equity compensation or look at a way to get equity in the company in return for an investment but I am not sure how to approach it.
It's unfortunate that this wasn't discussed beforehand, but you have to deal with what is in front of you now.
It's probably unreasonable for you to expect 50% equity in a company that hired you under these other arrangements. As far as I can tell, you are on track to get your increased salary in 5 months - fulfilling all their stated obligations. It would be very unusual for you to get the same amount of equity as the founder. However, it's not unreasonable for you to ask for something in exchange for your hard work.
Since it's only the two of you, why don't you simply sit down and have a discussion? Explain, just like you have here, that you feel the effort you are putting in deserves some sort of compensation beyond just salary, and that you think an equity position is warranted.
Be prepared for you want to react when your friend responds. He could say "No equity at all", "How much equity are you looking for?", or "How about x%?". Be ready to hear and understand any of them and know what you will then say (for example, "Let me think about that.") You don't want to get angry and just quit without exploring all the possibilities first.
If I had known that I would be taking on this much of the work for the companies when I started I would have asked for some sort of equity compensation to make up for the low salary and significant contribution.
So now you have a better idea now of how much work is involved, and you can revisit the arrangements.
Talk about it with your friend, and be open to all the possibilities. Equity might be one outcome, but there are may others (such as hiring others so that you aren't taking on this much work).