I know mountain bike frames are more robust but if I replaced my frame each time it took a hit due to me coming off then I'd have a cellar full of old frames. This includes a lot of stupidity.
Yes, it's wise to have the frame checked by someone who knows what they're doing and it is possible for damage to be there that isn't obvious to someone who doesn't know what they're looking for such as cracks in a weld or the head tube being stretched by a frontal force (see next para) but a side force on the entire frame shouldn't put too much stress on it, it will drag the wheels sideways putting a stress on them that they're not designed for.
A head on would put a sudden force through the forks which would introduce a rotational force into the head tube putting stress on where it joins the frame, from the description given by the OP I don't think this has happened.
Frames are more resiliant than you might think - the exception being carbon, which while being very strong, requires the entire structure to be sound, alu or steel can cope with a dent or two being present.
Yes, it plays on your mind, I had someone go over my motorbike with a fine tooth comb after I got rear ended at some traffic lights and knocked off, the AA came out and checked it before I rode it carefully home and then a trusted mechanic before I repaired it.