I don't think I'm going to move forward anymore with the Institute, as a glitch has occurred in my previous question! But is it worth actually trying to fix this? Do I really need the Institute or do I become an enemy and continue on as I can't fix the glitch I don't think?
Depending on how far you've gotten with the Institute, you can change factions up to a point. See this answer for a list of all the quest you do with each faction that permanently locks you in with them. In the case of the Institute, if you have not started Mass Fusion by speaking to a girl named Allie, then you should be able to change over to another faction still.
From that same answer:
The Molecular Level quest both is and isn't a point of no return, fundamentally it requires you to make a choice - what you do need to consider is that speaking to a faction will provide you the infiltration quest for the Institute but also make the equivalent quest for the other factions unavailable. It is possible to reconnect with the factions you didn't choose after completing Institutionalized though.
The Molecular Level can be misleading into making one think that whoever you initiate the quest with will be who you are stuck with. For that reason, I recommend you read the answer linked above to get a better understanding of when the real "point of no return" is for each faction (it's too much to repeat here).
To further explain, the game has multiple endings depending on who you ally with. Because of this, No, you do not have to have the Institute to complete the game. You'll find out what happens if you decide to go with another faction!