Should I refinance from 15 to 30 year mortgage to lower monthly costs?

Just over a year ago I purchased a starter house and was convinced to go on a 15 year mortgage as an "investment opportunity." This seemed logical, but my fixed costs have gone up over the last year (health care costs, etc.) and with the large mortgage payment plus home utilities eating 70 percent of my take home pay I do not have much left over to save. I am unable to commit to other loans, like buying a newer car (which I need), due to not being comfortable with taking on any more monthly payments.

A financially savvy acquaintance suggested I should view my current starter house as more of a temporary situation and I should try to refinance to get a lower payment and start saving (make extra payments as able instead of being locked into high payments). They said when I go to buy my next house it would be better to have $30k in the bank than an additional $20k invested in this property. So I am wondering if I should be trying to get refinanced to a longer term loan for this reason. The other thing is that since my savings are low and not building much right now (due to high loan payments), I don't have a lot of money to cover closing costs on another loan. I have heard that some loans can wrap those costs into the principle or something like that so you pay little up front. Also, because I was a novice I did not get a very good rate for my 15 year mortgage, so even with the rates going up recently I probably won't have too much higher of an APR than I currently do.

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