I wasn't sure how to read this chart, so I'll just say everything I see and hope that some of it is helpful to you.
The main problem was I wasn't sure whether to put you as 1st house or 7th house.
If we put your son as 1st house he is in the 11th with his friends. Also with moon and sun, a man and a woman, which could be your mother and brother?
Mercury is retrograde, which in horary can mean "going back" to an earlier situation. This could mean going back to his previous school or it could mean going back over a decision you previously made.
If we take the 3rd house to be your son's present school then that is ruled by the moon. In this chart it is combust, being next to the sun. Currently mercury is conjunct the moon, it is moving away, but when it turns direct again it will go back to conjunct the moon.
The moon is coming up to conjunct uranus. We're not supposed to look at uranus in horaries, but I always do. So there will be some change, either regarding a woman signified by the moon, or in regard to the school itself. I don't know how relevant this event will be to the overall answer.
The new school would be the 3rd of the 3rd, the 5th house. This is ruled by virgo, perhaps signifying that a public school would be more utilitarian than the nurturing cancerian school he is in now. This is ruled by mercury, mercury already comes into play as the significator of the 1st so this is one reason why this chart confused me.
The only planet in the 5th house is saturn, although it is very close to the end of the 5th house. This could mean austerity and harshness in the new school, it could also come into play as the ruler of the 8th house, which is either other people's money, or if you are signified by the 7th, your money.
It could also signify that your concerns when you drew up the chart were your responsibility to your child and problems in that area.
Saturn is inconjunct mercury. Inconjuncts in horaries signify to me that a person is undecided. This shows that you are in 2 minds about the option to move to the new school. If your son is signified by mercury he would also be in 2 minds about it.
Generally in my experience when I've had inconjuncts influencing me I have either decided not to do that thing, or I have done it and it has turned out not to be a good thing.
The sun and the moon are square pluto in the 8th and inconjunct saturn, ruler of the 8th. This shows that the sun and the moon are not happy about the 8th house matter, but I am not sure whether the 8th house signifies your money, or getting some financial help from somewhere else, perhaps asking someone else for money.
The end of the matter, the 4th house, is ruled by leo. So it will be decided by the sun, whatever that signifies. Perhaps it represents you as mother of the gemini student or perhaps a significant man or a significant leo.
You've also got neptune and chiron in the 10th. That could mean illness of a parent or it could mean loss of a job. I don't mean to scare you. It might not mean any of those things since they aren't the focus of the horary. But in my experience they have meant those things.
The moon also rules the 2nd house, so when it reaches uranus (after 2 days, 2 weeks or 2 months using Noel Tyl's system of predicting timing) you could have an unexpected change in income.
Also my mum always told me with mutable ascendants it means that the situation is "in flux" and the situation could change.