I've always been told not to use tampons or have sex until I'm done bleeding and to stick with just pads because putting anything up there before that could lead to an infection. I have always waited to dtd again until I am sure I've been done bleeding for at least a few days and I've gotten a negative hpt. That being said though, my miscarriages have always ended with a few days of spotting and then nothing after that until my next cycle. And because I've either had blood work being done or am using hpts to track my hCG levels dropping pretty much from the start so I know if I am still getting a positive.
What I am guessing happened is you were on the tail end of the bleeding and then dtd caused uterine contractions that are now expelling the very last of the bleeding, hence the new bleeding. As for whether or not you could get pregnant again right away, that's something that can only be known with time. It's very unlikely that you will get pregnant if you still have enough hCG left in your system to show a strong positive on an hpt since you typically won't ovulate again until those levels have dropped enough. But it's also not impossible either. Many women, including myself, have gotten pregnant again right after a loss without a period in between. Usually getting pregnant again right off isn't an issue but there are a few circumstances where it's best if you don't. However, with those situations, your doctor would have told you not to get pregnant and the reasoning for why.
I would think you'll be fine and most likely won't get pregnant until your levels have dropped low enough. For me, my cycle doesn't restart until my hpts are BFN again and my next period is delayed by a few days to a few week but some women will ovulate while still getting a light positive and having slightly elevated hCG levels so they get their first period right on time. But if you aren't wanting to get pregnant again before your hCG levels drop or anything like that, then I would recommend using protection and abstaining at least until you've had a few days in a row without bleeding. If you aren't seeing your lines on the hpts lightening up with time, then I'd contact your doctor as that can be a sign that you have retained tissue. It can take a few weeks for your levels to drop so I'd get a few more tests and check to see what the lines are doing every 3-4 days. As long as they are getting lighter, then you're most likely okay.
Good luck.