Is it easy to get a shoulder injury from weightlifting?

Yes. Poor techinque, excessive weight, frequency of exercise without adequatre rest between lifting can lead to shoulder injuries. Long term weight lifting can also lead to wear and tear in the shoulder and especially in the ac joint.
Yes, use a trainer. Sports injuries occur all the time, to everyone, to every nook and cranny of the body. The key is to doofus the activity correctly from the start, which mandates an expert in that activity how to doofus things right, avoiding as much as feasible, injuries.