I'm kind of nervous because I was sitting on the toilet and my penis may have touched the underside of the seat, but then what happened next was disgusting. When I looked down my penis had a decent amount of a clearish gelatin substance on it (I think coagulated might be the right word). I then pulled it off with toilet paper and checked on the bottom of the seat and there may have been a wettish spot on the toilet. A little bit later I had a shower, but now I am really worried because I looked up on the Internet if semen becomes gelatin like, or coagulated when left out in the open and apparently it does. I am really worried that if it was the semen of one of my brothers or dad, if it could give me an STD or STI or something or cause problems if I ever get married and have sex. What do you think?
Since it was clearish and not an opaque whitish color, I will assume that you found pre-ejaculatory fluid on your penis. That fluid tends to dry fairly quickly, so the fact that you found it still in a liquid state would lead me to conclude that it came from your penis and not your brothers or your dad.
Yes, it is disgusting to come into contact with someone's bodily fluids, but before you can contract an STI, the person's whose fluids you came into contact has to have the disease. I'm going out on a limb, but I suspect that it isn't very likely that any of them have an STI. If you ever did contract such a disease, it would be rare that you would not notice some symptoms. The reason STI's spread so much is that many people ignore the symptoms at first.
Therefore, I would not jump to conclusions based on imaginative "what if" situations. Instead, I would like you to make sure the toilet seat is clean before you use it and then take note if you see dripping of a thick clear fluid from your penis when you are done. It may not happen every time, but if you do notice it, then you can put it down to the fact you are getting older and are starting to produce pre-ejaculate fluid now.