is he cheating

My husband goes out of town sometimes. Well when he does he doesn't call or text me very much. Always says he doesn't have good service .. ( but when I look at the phone bill he talks and text everyone but me )
Well the last time he went he left at midnight so traffic wouldn't be so bad on his 12 hour drive. 3 days later ( we barely talked ) I asked why he hadnt called. He said is phone was dead that day.. so I decided to look at the bill online. He was texting a woman ( who was in the same town as he was ) she started texting him the night he left at midnight and they text all day and night for 3 days straight. ( the started texting in Oct 2016 ) but this month it was out of hand. 1074 times in one month . There is only 124 to me.he claims it was just talk and nothing else and doesn't now why it upsets me so bad.but he deleted all their text. After i told him i wanted to see them. He asked me for some pics of his work. ( he's self employees ) cause this guy wanted to see his workmanship. So I sent him 3 pics... he sent them to this woman.. when I asked him why he lied about that he said cause I knew you'd get mad.. he was even texting her the whole time 2 days before he left. I noticed when he came home and was getting out of the shower that he's even shaved down there.. ( something he doesn't do often ) and when I asked he said " I done that a month ago " and he's gonna keep doing it while it's hot . But he hasn't since he came home 1 1/2 months now.
She is married with 3 small kids. We have been married 20 years and with grown kids from other marriages.
She has text him 10 - 15 times since. And he doesn't respond.do you think he's done anything or was it just talk ?? I thought we were happy . We hardly ever fight. Maybe 3 or 4 times in 20 years. He swears he loves me more then anything . But yet if we keep fighting over this he'll leave..