From what I heard if you got a positive on a HPT that you should also get a positive from a blood test. From what it sounds like, your dr isn't monitoring you like you want them to. I strongly suggest to at least get a second opinion!
My last pregnancy I decided to go to an OB (I had a family dr last time, and since moved, but wouldn't have used him again anyway). The OB never took blood work or did any tests on me, just the initial exam. If he did he would have found that I was miscarrying instead of finding out 5 weeks after the baby passed. The point of the story is I decided to find another dr/midwife. I went with a certified nursing midwife who will test and ultrasound at the visits, etc for all patents, and do even more for those who need to be monitored more closely. I'm not pregnant yet, but I know she'll do what needs to for my (and the baby's) health.
Your paying them, find a dr that will go the extra mile for you since you are high risk!
Also, every pregnancy is different, and it's possible you may not be feeling any symptoms yet either. With my first I was so tired I couldn't get out of bed (child is now 20 months old and healthy), and with my second one I wasn't tired at all, I sort of felt like I had more energy and didn't get tired until I was miscarrying. A friend of mine, her first pregnancy she wasn't tired at all, for the second she just wanted to sleep 24/7. The lack of symptoms shouldn't be a sign of not being pregnant. I have heard of women who didn't feel any symptoms until later in pregnancy as well (and had healthy babies). Everyone is different, and everyone's pregnancies are different.
Also, from what I read, every womens cycle is set number of days (for them) from the day the ovulate until the day of the next cycle. So if you normally have 14 days from the day you ovulate till the first day of your cycle, and your past those days you need to get it looked into. Have you asked why there getting negatives when you get a positive on your HPT?
One last thing, I have heard of some women who have a positive test, then later get a negative and get AF a week or so late, and they just had an early miscarriage. That's the only time I've heard of "false positives" (Other than some medications causing them like IVF).