don't they basically mean the same in my sentences?
In a loose sense, yes, but they have subtly different connotations.
February 11 was really hectic, so I had to do a ton on the day.
This (potentially) implies / emphasises that you had much to do on that day, as opposed to stuff you could have done beforehand. Example: "the product launch was such a last-minute effort, we had so much to do on the day"
February 11 was really hectic, so I had to do a ton in the day.
This (potentially) implies / emphasises you had to do your stuff in the day as opposed to in the evening or night.
February 11 was really hectic, so I had to do a ton during the day.
This (potentially) implies / emphasises that you were busy throughout the (whole) day rather than having a short burst of activity.
Besides these nuances, I would tend to agree with @Jay that none of them sound natural. The main problem in my opinion is that the "so" construction is backwards. You didn't have a ton to do as a result of February 11 being hectic. You deemed February 11 to be "hectic" as a result of you having a ton to do.
Therefore, from a formal written grammar perspective, I would expect something like "February 11 was really hectic, since/as/because..." instead of so. In everyday speech, there would probably be no word there at all, just a comma or semicolon.
In terms of naturally idiomatic speech, I would also probably replace on/in/during with that. Finally, I would probably rearrange the words a little further, and end up with
February 11 was really hectic, I had tons to do that day.
Although at this point it is probably getting very subjective (according to Br.Eng / Am.Eng etc) which is the most "natural" phrasing.