Trying to hand-solder fine pitch SMD chips without good flux is very difficult even for an expert. Personally, I like a liquid R or RMA (rosin) flux, applied with a small brush, as applied sparingly the residue does not need to be cleaned up, but many will swear by synthetic or rosin gel fluxes applied from a syringe with a needle. I don't like flux pens much for rework as the tip tends to get torn up on rough surfaces like existing joints. Whatever you do, don't use paste flux in a tub or tin from the hardware store as most such fluxes are far too aggressive and their residues will corrode the tracks off your board and the pins off your chip.
With flux, the surface tension of the solder acts to pull it back to the pin/pad area, breaking any bridges unless far too much solder was used. Simply applying flux to the pins and pads and reheating them several at a time with a freshly tinned and wiped bit, removing it outward with a dragging motion towards the tips of the pins should leave you with no bridges and, if there was an appropriate amount of solder present, with acceptable joints.
If you need to remove excess solder, wick it off with a fluxed fresh piece of wick. When cutting back the used end of the wick to get to fresh wick, always bend it to find how far the solder wicked up it and cut it back leaving a couple of mm, but no more, that has solder wicked into it at the end for better quicker heat transfer when you apply the iron to it and the joint. Wick oxidises readily and if its too old may be unusable. A year or so isn't a problem, but if its visibly tarnished or decades old its useless for fine work.
350 deg C, or maybe slightly hotter would be a good temperature to start with. 250 deg C is far too cold and 450 deg C is far too hot. Except under exceptional circumstances stay in the 315 to 375 deg C range. Cheaper irons with poorer thermal coupling to the tip or less power delivery tend to need a slightly higher setting within that range, as do many unleaded solders.
Search Dave's EEVBLOG videos for 'drag soldering' to find out how to do it right in the first place.