Well, I'm not a native speaker of English -

but this doesn't sound quite "right" (i.e. idiomatic) to me at all.

It doesn't even sound natural with commas to me.

I would only worry about variation if you have used "also" already in the same sentence or the one before or after. Otherwise, it is such an unremarkable word that it would not stand out as being repetitive if you use it twice in a paragraph or something.

Some other possibilities might be:

She had a brief relationship with Marc. Furthermore, she had a relationship with my best mate Tom.
She had a brief relationship with Marc. What is more, she had a relationship with my best mate Tom.
She had a brief relationship with Marc, and another/ a longer relationship with my best mate Tom.
She had a brief relationship with Marc, as well as a relationship with my best mate Tom.

I'm repeating "relationship" here as I guess it is a rhetoric device?

She had as well a relationship with my best friend Tom.

I'm afraid that sentence does not only sound 'not quite right', it is incorrect.

You could say "As well as that, she had a relationship with my best friend Tom" (although it sounds a little clumsy.)

One variant would be the one below (with my suggestions in bold):

In her youth, she was a real cutie. Consequently/As a result/For this reason/This meant that she was always in a relationship. She had a brief relationship with Marc, as well as having had a relationship with my best mate Tom.

Other than that, CM2DD's suggestions are also good.