Also, stringing sentences together with “and” to force them to be a single sentence is not exactly good writing.

And you have a number of examples here of bad writing. It isn’t necessary to begin with a conjunction. It adds nothing to this sentence, so delete the “but”

Being around a friend who is constantly “snuggly” is one of my biggest sensitivities.

If it is a couple you’re talking about, I would say so:

Being around a “snuggly” couple is one of my biggest sensitivities.

Next sentence:

Whenever I would bring it up to him the conversation would always go off on another tangent, with my friend and I arguing.

with is a preposition and its objects are friend and “me”–you don’t use I in the nominative case here, but ME in the objective case…

Whenever I would bring it up to him, the conversation would always go off on another tangent, with my friend and me arguing.

You don’t need conditional here; it works better in present tense:

Whenever I bring it up to him, the conversation goes off on a tangent, with my friend and me arguing.

The prepositional phrase at the end is weak, so I would change it to:

Whenever I bring it up to him, the conversation goes off on a tangent, resulting in an argument.

Now, putting the sentences side by side:

Being around a “snuggly” couple is one of my biggest sensitivities. Whenever I bring it up to him, the conversation goes off on a tangent, resulting in an argument.

Now we’ve lost the connection, so I rewrite to get this final result:

My friend knows that being around a “snuggly” couple is one of my biggest sensitivities, but whenever I bring it up to him, our conversation goes off on a tangent, resulting in an argument.

“I know we would all feel more comfortable if you would use this…first night on me, but up to you after that “