It's a conditional phrase. You might think of it as being the same as
...if we are interested
So your original sentence means:
I've given your information to other people, and if we are interested,
someone will contact you.
There are a few common idioms or sayings that fit the situation rather well, though they do not mean exactly “having so much [work] because you chose it yourself”.
There’s “You made your bed (– now lie in it/you are going to have to lie in it)”, which means that the person you’re talking to has created their own mess, so now it’s their own responsibility to fix it.
Similarly metaphorical is “You reap what you sow”, which compares the bad situation to a field—if you sow bad seeds, you’ll reap bad grain; likewise, if you ‘sow’ a bad situation for yourself, you’ll have to ‘reap’ the consequences, no better.
More direct and pragmatic, “You asked for it!” is used to indicate that someone should not be complaining about their current situation, since it is only what they themselves asked for in the first place.
Even more direct is “You brought this on yourself”, which does not mince words and simply says that the person addressed caused their own misery themselves.
Note: All of these could be considered somewhat rude—their intention is to be blunt. If you wish to be softer and more polite about it, I don’t think there’s a fixed expression available that fits. Instead, I would just phrase it in a natural, but polite, way; something like, “I’m sorry to hear you’re so caught up in work—but you mustn’t forget that you did ask for quite a heavy workload, so you really only got what you asked for”.
An idiom that is a bit less rude would be Be careful what you wish for—you might get it (or it may come true, or lest it come true; there are several variants), which quite properly warns someone not to want or ask for something without first thinking through what actually getting it will entail.
Best Answer
The way your question is posed shows that you're thinking about it wrong.
It's not the case that "some of these sentences take will and others take to".
First, it's the Verb (not the sentence) that "takes" a Complement, and every verb is different.
Second, expect can take both infinitive and tensed (that) complement clauses. Other verbs differ.
Third, the grammatical sentences with will above don't have that, but it's allowed --
these are correct, because expect, think, and know can all take tensed complement clauses:
so the complement clauses with will are tensed clauses, not infinitive clauses.
That means that the reason why you can't say no. 4 is that you must use he and not him in
Fourth, on the other hand, the complements with to are infinitive clauses, not tensed clauses.
To is a marker of an infinitive; it's not a verb but a complementizer, and it doesn't mean anything.
And the subject of an infinitive must be objective -- him, not he -- so that's the reason no. 5 is bad.
The sentence below works because expect, tell, and want can all take infinitive complement clauses:
This is a fact about the verb expect, by the way.
If you try the tensed (that) clause examples with tell or want instead, you'll get ungrammatical sentences, because tell and want can't take tensed clauses with that. And if you try the infinitive examples with think or know, the same thing will happen, because think and know can't take infinitive complements.
Grammar is not about words following words; grammar is about constituents, mostly clauses.
Get that right and the rest will follow.