My 3 month old puppy pees and poos normally but she still tries to pee and nothing comes out.  Do you think this is an infection or habit?  I know, go to vet, but I've got stung once too often.

Sounds like a possible urinary Tract Infection and antibiotics would need to be prescribed by your vet.
Don't mess with kidneys and THAT is the next stop up the urinogenital line from the urethra.

I agree about Vet but just a thought, do you treat her when she pees? May be she is trying to get a treat by pretending to go. Seeing this with neighbours who are housetraining by giving a treat when she goes outside.
Their puppy now 'wants' to go out so often as she knows food is involved!

I don't normally housetrain pups with a treat just lots of praise. However, with the 'last' wee of the day, I settle the pup down for the night with a biscuit to occupy the pup when she is left for the night. Being the breed she is (GR), Isla cottoned on very quickly that she would get a biscuit at this time, so she would spend the evening asking to go out, squat for a second, then shoot back into the house and into her crate and sit there looking very pleased with herself. She was only 11 weeks old when she started doing this.

She sounds like a typical intelligent Golden!

I have two grown up Bernese who this year became masters of the "Pretend" pee at bedtime !! It took me a little while to cotton on (obviously not so bright as they are !!) but we now have got the measure of them... It took a few evenings of determination on my part to go and look for the wet patches before we went in for bedtime bonio's

Unproductive peeing would normally suggest a UTI, or even bladder stones, although at only 3 months, that's unlikely!   Collect some urine and take it, with the puppy (fresh) to your vet and get him to run a urinalysis.

If you don't trust your vet, and the vet-client relationship has to be one of trust and communication, move on.   This shouldn't be a case of cost however.

Funny treat rewarding is mentioned because with my current two, last thing they are taken out to empty and brought back to their beds with a biscuit treat.   Just lately my Whippet has been ready to leap into her crate and have her biscuit only to sit there and look 'worried'.   Letting her out again produces a BM and not just the pee she does.   Clearly she's after the treat first!!!   Hum.   And she is flippin bright - too bright for her own good!

I have nearly always found mien will squeeze out something to get a treat when I am housetraining LOL