I tried this:
Seemed like everything I'd been doing recently was to follow people around.
Is that correct?
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No, but I think you may well hear it said like that.
Let's switch up the order of the sentence:
Following people around seemed like everything I'd been doing recently.
In this order, we must use following since the verb is the subject of the sentence.
Likewise, imagine we respond to the question "What have you been doing recently?", we would simply say
Following people around.
Certainly not "to follow people around".
So, you should say:
Seemed like all I'd been doing recently was following people around.
Lastly, I would say "everything" doesn't sound great here. I'd be much more comfortable with "all".