Hey and welcome to the forums
Thanks for posting a video, it's always nice to see what and how are other people playing. You're doing fine for just 2 months time.
What you could do to instantly improve a bit is to focus a bit more on your bow hold. I notice that your pinky is over the adjusting screw and touching it from the inside. Your pinky should always be on top of the stick and slightly curved as to avoid tension, then you occasionally transfer some load on to it like a lever to lift the stick when you don't want to use its full weight. Also your thumb needs to be curved and not straight, when it's straight you're prone to build up some tension which could affect your bowing.
At first I didn't think it's that important either, but it's amazing how much of a difference even the slightest adjustment in the bow hold can make. A good exercise to do is to place the middle of the bow on the strings with its full weight, then start doing full bowing motions all the way to the tip and back to the frog while trying to keep the exact same weight on the strings as they had when you just placed it on in the middle. To accomplish that you will need to slightly press down with your index finger when near the tip and slightly press down with your pinky to lift the bow when near the frog. Your goal with the exercise is to be able to seamlessly transition between the two and keep the same pressure throughout the whole bow.
Another thing that will greatly help you is to start using your elbow, replacing most of the shoulder movements that you do. The only shoulder movement you should have is the up / down movement of your upper arm for changing strings and a very slight forward and backward movement ONLY when playing in the bottom few inches of the bow (next to the frog). Once you go a bit past the winding on the bow your elbow and wrist should completely take over and your shoulder should not be moving. Just imagine extending your elbow away from you as if you were trying to pull a sword from its sheathe or something, you know.. that 'reaching' motion, because you have to do it in a straight line
Hope this helps
Also I made a really easy tutorial for O sole mio that has a piano track as well in the 'Share' topic in case you want something easy to practice with some backing to keep the rhythm.
When you hold the bow, you should be able to lift both your index finger and your pinky off the bow completely; the thumb and your middle and ring fingers should carry all the weight. Your index finger and pinky will be on the bow when you play, but their purpose is to adjust the balance of the bow.
Another thing: once you have the bow hold, always think about leading with the wrist and keeping your hand loose. When pulling the bow downward, your wrist should lead downward; the friction of the bow on the string will pull your hand upward, and the hair of the bow should be flat against the string. On up bows, pull your wrist upward and again let your hand trail behind; the bow should be tilted so the stick tilts away from you. The whole point of this is to always pull the bow up and down, not press it into the string.
World's Okayest Fiddler