It's very nerve racking when you're first diagnosed and the re-occurring trips to a hemotologists office to keep getting blood draws allows us to build up all kinds of scary things in our minds.
First of all, your beginning of the ITP journey if very normal. Most of us went in for some other visit and a random blood test showed the low platelets. ITP is typically a diagnosis of exclusion rather than immediate, so they start with a basic set of blood tests and when it comes back as normal or inconclusive they order up another set. When they've ruled out the other conditions that also cause thrombocytopenia like luekemia, HIV, Hep C, etc, then they make the ITP diagnosis.
For now you're slightly below normal (140 to 340), but unless you have lots of bruising, lots of red dots under the skin (petichae)or nose bleeds that you can't stop in under 10 minutes it's not likely you have be overly concerned. Most of us had mild panic if we had these types of things until we had a few rounds of blood tests and hemo visits under our belts. Steve (Gort) had some excellent advice that was sticky noted on the Newly diagnosed forum:
www.pdsa.org/discussion-groups/5-newly-diagnosed-a-frequently-asked-questions/8344-excellent-advice.html
While the drop from 120 to 102 was scary to you, the old timers here are all wishing we could be that high. As Erica says they can do emergency surgery at 50, and most don't treat until we're under 20 or 30. It's not uncommon for platelets in "normal" people to flucuate 30K in a single day, so you may go in next visit and be up.
At counts above 50K, most of us only see our hemo's every 6 months. I went that route for 15 years before I had to start treating. We do call and get a blood test if we notice symptoms like I mentioned above. Definitely have the discussion with your hemotologist about your concerns and see if you can arrange to have a blood draw if you feel you have symptoms. And it's okay to freak a bit, my funniest one was when I put a new set of sheets on the bed without washing them and had a rash from the sizing. Even though I suspected that was the cause, I didn't feel comfortable until I got the CBC results. You'll have stories too and can come here and we'll understand and all have a good laugh or cry together.
At this point, it's a good thing to start building a relationship with a hemo so that if you do get under 50 you've discussed treatment options, your life situation and the impacts of the various options. Then if you have to treat, you're not making decisions from a more stressful place or being rushed. You do have to remember that most hemotologists are also oncologists who see cancer patients with far more critical issues every day. They seem very laid back when they say oh, just come back in 6 months when it's consuming our thoughts, but to them it's minor and treatable. If you're not comfortable with your doctor, then fire him and get another, it's okay. Many of us have been through a few until we found one whose style and office worked for us.
Our best advice, don't let ITP consume your thougts. Become knowledgable, but don't obsess with the web searches, only take Web advise from reputable sites (medical schools, etc) and enjoy life and your daughter, she'll only be this age once.