Exist in and feel those emotions, and then let them go as much as you can. As others have said, time will heal this wound. Don’t run into the arms of someone else or try to numb this pain; it’s important you feel it. Rushing into another relationship will only bury this pain by putting you in an unhealthy situation; numbing it will only lead to bad decisions and possible substance abuse. Let yourself feel this way, as horrible as it feels, and understand that it won’t be forever.
You will be okay, and to be honest you will probably be more than okay. In a period that seems impossibly long now but laughably short at the end of this, you will become a better, stronger, and healthier person with a greater capacity to love and the wisdom of who better to give that love to. It is difficult, but you will survive. And then you will thrive. Love yourself and ride this out. You got this.
Definitely hang out with people and try to have fun, it’ll help take your mind off things and begin to remind you who you are outside of the relationship.
But I’m curious why going on a walk with a friend in nature would be cheating? Hanging out alone with someone of the gender(s) you’re attracted to isn’t cheating. While everyone has different definitions of cheating I think most would agree that violating your partner’s boundaries around sexual, emotional, or romantic intimacy is usually what constitutes cheating; hanging out with a friend in a purely platonic way isn’t cheating and if your partner made you think so that’s a bit of a red flag in my opinion.