Me and my guy are in a long distance relationship. Inshallah our nikkah is supposed to happen within a few weeks but we only meet once a year. Due to financial difficulties, we can’t move in together yet and have our Walima. I heard if I don’t have sex with him after nikkah within 24 hours, it will be bad. Another person told me if we don’t have sex within 4months, it will be automatic divorce. Please help me.
No it is not obligatory. The Quran mentions marriages that have not been consummated yet, such as:
إذا نكحتم المؤمنات ثم طلقتموهن من قبل أن تمسوهن
when you marry believing women and then divorce them before you have touched them ...
وإن طلقتموهن من قبل أن تمسوهن
And if you divorce them before you have touched them ...
وربائبكم اللاتي في حجوركم من نسائكم اللاتي دخلتم بهن فإن لم تكونوا دخلتم بهن فلا جناح عليكم
... your step-daughters under your guardianship [born] of your wives unto whom you have gone in. But if you have not gone in unto them, there is no sin upon you.
It is implied that a reasonably period of time would have passed in which a person can change their mind.
Similarly the Prophet ﷺ consummated his marriage with Aisha after three years of contracting Nikah. Similarly there are traditions that there was an interval before consummation of the marriage of Ali with Fatimah.