Assets:
One '98 hatchback (bought used, paid cash).
<1k savings
You need a bigger emergency fund. Something is better than nothing, true, but I'd want a bit more than that.
Rent - $400
Utilities - $80 - varies, this is a high estimate. I split cable, water, gas, etc. with 4 other roommates.
Is $400/mo rent with four OTHER roommates the best you can find? $80/mo split five ways also seems a bit high, though I'm not sure how you can reduce that (they may not be too happy you're not paying your "fair share" if you decide to stop watching cable and refuse to pay "your" portion).
Food - $150
Dining out - $0
Alcohol/bars - $20
More room for improvement. I'm not sure about food costs, but I'd expect you could get the food down to $100/mo (our family of four spends about $100/wk, and personally I think we're still a bit wasteful). Alcohol is also not a need; if this is just to socialize, find cheaper ways? Yeah, $20/mo may not be much, but it's the $50 plus $20 plus $100 plus $10 plus...that can really make a difference.
Car insurance - $40
Gas - $60
Misc. car expenses - $60
Insurance seems reasonable, though that's no reason to not occasionally shop around (I'd at least have a cursory glance at other policies each time you have to renew). Gas...I dunno, just don't drive it unless necessary? Sounds like you're already trying to do that. $60 for misc car expenses, are we talking saving for the inevitable maintenance/repairs? If so, that sounds pretty reasonable, though I'd want you to have a decent emergency fund in case it needed a new transmission or something else that could catch you off-guard.
Clothes - $10
Gifts, pharmacy, etc - $30
Buy all your clothes at thrift stores, and don't buy anything unless it's necessary. Yes, $10/mo sounds good, but if you purchase on dollar days (or whatever the equivalent is), that's ten shirts/pants/coats/etc.
Explain the pharmacy...i.e. why is it grouped with gifts? Do you buy tylenol (or rather, generic acetaminophen) for Christmas presents? Medicine you actually need = ok, but you could drop the gift spending to $0 if you desired.
or how to stop panicking about the fact that I'm saving less than $200 a month?
If you were putting a full $200/mo into savings each month, it'd take just over four months to save up a month's worth of expenses. That's not too terrible. If you cut out alcohol ($20/mo), reduce food by $50/mo, cut out gifts (I'm assuming gifts was $15 of your $30), and drop the clothes to $5/mo, that's another $90/mo right there. In 8.5 months, you'll have an extra month's worth of expenses saved up just in savings alone (remember, $90/mo in savings is also $90/mo in reduced expenses; your monthly expenses would now be $760/mo).