It doesn't *help* your case that you said you weren't injured, but I am a lawyer doing these type of cases and find that about half of the people I see said that and then go to urgent care the next day and then go to a chiropractor for 3 months. What they usually mean by "not injured" is that they didn't break a leg or need stitches.
Just call the claims rep ("Adjuster"), and say "I know I said I wasn't injured, but I haven't been able to sleep well since the accident and have been distracted. I lost about X hours of productive work time this week, related to this accident. I realize that isn't a serious injury, but I feel like I should be compensated for the stress, pain, and anxiety this has caused me. Could you offer me $X,000 for that?" They might negotiate down, so start higher than you'd accept. They might try to argue with you, or say they need medical bills/records. You can just say that you don't think you need any medical treatment, but this has impacted your life. This is a great time to practice negotiating for your next used car purchase.
Do know that once you accept a number it will be really hard to fight that (If they send you a check for $500, you can't go back in 2 weeks and ask for more.)
Lawyers usually take a 30+% fee off of your settlement, so it isn't worth it unless they completely refuse to negotiate with you or you have a lot of expenses.
Gather proof if you have any, especially of the lost work. If not be prepared to talk about using ice, heating pads, advil, or other pain killers.
If your accident totaled your car with a side swipe and happened at 20 miles an hour they WILL expect some bodily injury. They routinely see people in 10 mph parking lot rear end accidents getting treatment for a few weeks. I think a number above $1,500 would require some proof and would be harder. I might start with that number, aiming to negotiate to $750 or so. (Of course if you have proof of your lost wages, I'd expect more.) If you have actual lost wages or medical treatment expenses try to negotiate for a settlement of 1 to 2x that amount.