I do not think it is likely you hurt the deltoid. i think you were spot on with your biceps area. Poor technique, too much weight most likely caused the problem. You do not mention you have been given any advice from e.g. a personal trainer but that you try to sort the problem out yourself. Well unfortunately that is (and you know it) possibly the road to disaster. You mention you ignored the problem and then have tried to solve it by not training and rightly you assume the problem will return when you re-start. I think you are right on this.
If I were you I would get professional advice on technique.
The reason is that your problem islikely a joint problem. Around the shoulder we have a so called rotator cuff(Infraspinatus Teres Minor, Teres Major, subscapularis suprapsinatus) which ought to keep the joint parts in position so the strong muscles as Pectoralis, Lats will not pull the parts of the joint apart and cause e.g. a subluxation of the joint (and/or more serious problems like labral tear of the anterior capsula). Now if you think is this it. No it becomes more complicated as the position of the shoulder joint (Gleno-Humeral) is affected by the position of the Scapula. Now if you have protracted shoulders (most people who work out in gyms do) and internal rotated arms (your thumbs point towards your body and not forewards at rest) You have to assume that the positoning of the shoulder is incorrect and thus the starting position on loading wrong. Next problem can be the general posture (ears at rest should be more or less over shoulders and not in front) of the spine.
Ok do you still think YOU can fix it? In that case: back of from your Pecs exercises, from your Lats exercises and from you Upper traps exercises. Start working on posture, maintaining posture during loading. Train rotator cuff and Scapula stability BEFORE you even think of doing bench presses. Given this 4-6 months and try again. Personal I think you ought to see a Physiotherapist and/or a personal trainer to given advice (or risk to do yourself serious harm and great a orthopedic consultant in the near future.
Hope this helps. I don't think this is what you would like to hear but my experience tells me that the majority of people in the gym have no clue what they are doing.