Before you spend any money on an electrician, contact your electric utility. Explain that you are experiencing power quality problems, bright and dim lights, etc. and that you would like the utility to perform an investigation and monitor the incoming power. Most states require that utilities respond within in a week or so and perform an investigation free of charge. Most states require the utility to maintain residential voltages within +/-5% of 120 volts (114-126 volts); ask the utility to provide you with a graph of the recording to show that the incoming voltages are within tolerance. There could be a number of utility-related problems that could be causing your issues, such as an undersized transformer, bad neutral connection, undersized service wires, too long of service length, etc.

Once any utility-caused issues are ruled out, pursue contacting a licensed electrician.

Any updates on your dimming lights issue?