Make-, have-, and let-causatives use bare infinitives:
You made me check a dictionary.
You had me check a dictionary.
You let me check a dictionary.
But get-causatives are different. They use to-infinitives:
You got me to check a dictionary.
So there is indeed a problem with example 3; it is missing the infinitive marker to.
Semantically speaking, had-, let-, and got-causatives aren't really appropriate in your original context:
- Let is a permissive causative, but jonlink was not giving you permission to do something.
- Had is a directive causative, but jonlink was not directing you to do something.
- Got is an indirect causative, but jonlink was not persuading, inducing, or manipulating you into doing something.
- Make is a coercive causative, and jonlink's answer created a state of affairs that forced you to do something (check a dictionary).
The make-causative is the most appropriate choice in this case. You had to check a dictionary in order to respond to what he wrote, so the make-causative is the one that fits most closely―although the type of coercion involved is rather weak.
Although this is called a coercive causative, when the coercion is particularly strong, there is a tendency to use force instead ("He forced me to hand over my valuables at gunpoint"), which uses a to-infinitive.
I don't personally think using the pronoun you sounds rude, but if you wanted to avoid it anyway, you could do so by avoiding causatives altogether:
I wasn't sure what the plural of aspirin was, so I had to check a dictionary.
Phrasing it this way focuses on you, the speaker, and avoids mentioning the other person at all, so it avoids any possible offense.