Hoping - this happened to me on IUI #1 and #3. Sorry that it looks like you're experiencing a chemical pregnancy 
For your first attempt, I genuinely think you can see this as a positive thing (I did with mine), and that early testing was worth it because we now know that:
a) you created an egg which was fertilisable
b) you had IUI around the right time
c) your clinic did a good job of inserting the sperm and got it to the right place
d) the sperm found the egg
e) the egg implanted (you can't get a BFP without implantation)
f) your body started producing HCG like its supposed to
Those are hurdles that you now know work for you. Some women have to have many attempts before they establish that they've got a problem with one of these things.
Don't be too disheartened. You'll be better mentally prepared for a BFP on a future attempt and you've gained a lot of useful info from this attempt.
I would say don't throw your money down the drain having your clinic run blood tests or do a scan. You have had a straightforward chemical pregnancy which is very very common and par for the course in TTC.
I know it sounds like I'm belittling it but chemical pregnancies are so common that they barely figure for most people (because they don't know that it has happened) so try not to build this into something bigger than it really is, although of course its disappointing because life would be so much easier if you had success first time!