Should I raise the rent after information received from agent

[Robert Allen Lin]

I just purchased a property in Spring Texas. The listing agent simultaneously put the property on the market for lease. In the span of 2.5 weeks, there were 19 showings. Of the people who visited the property 7 left feed back. Four out of seven rated the property 5/5 for desirability and pricing just right. One person rated 4/5 with pricing just right, and another 3/5 with pricing too high. The last person was "maybe" interested in leasing with no feedback. 

I believe 1 person submitted an application, at least 3 were very interested in leasing. The agent has passed on the information of the tenant interested, at the listed 2,200/mo rent price. My question is, should I try to raise the rent and try to get a higher rent based on what seems to be interest in the property? Based on sold comps in the past 6 months, 2,200 is around the upper end of rent, so I'd be thinking an additional 50 bucks per month, 100 max. Is it irresponsible investing to not list it ourselves and try to get the best offer or use it as negotiating leverage? How should I be thinking about it as a first turnkey rental?