The basis of any good relationship is trust. If you don’t have trust then you don’t have a solid relationship. I understand that you do not want to lose this relationship but consider that your partner has lied to you in the past and may be lying again.
At this time he is not being fully honest with you. He refuses to show you his phone to prove that he is not texting other girls. He may not be texting other girls but he’s unwilling to prove it by showing you his phone. How do you continue a relationship when you can’t trust your partner? Trust has to be earned. He has given you no reason to believe that he has stopped cheating, especially in light of his current suspicious texting behavior.
When someone shows you their “true colors” then you must see them for who they are. People can change but it’s not clear that your boyfriend has or is willing to. If you continue to ignore his behavior and act as though he won’t cheat again (when he might be), then you risk getting hurt. You may be engaging in denial. Denial is an unconscious defense mechanism that protects oneself from uncomfortable facts.
I understand this may not be the answer you wanted to hear, but it’s unhealthy for you to ignore the truth. It’s also important to analyze why you may be willing to tolerate his problematic behavior. It’s virtually impossible to be in a relationship with someone you cannot trust. If I were your therapist I would be trying to understand why you may be willing tolerate this behavior from your partner. One explanation is low self-esteem. Another explanation may be that you’re not sure what a healthy and trusting relationship is like.
If you are having difficulty letting go of this relationship or understanding why it might be unhealthy, then you should consider therapy. I cannot say, based on a short letter, whether this is an unhealthy relationship for you. I suspect that it is. If you are in a relationship with someone who constantly lies and whom you cannot trust, then generally speaking it is not advisable for you to stay.
Lastly, I would suggest discussing these issues with a therapist. He or she can help you analyze the situation and advise you about how best to proceed. You may not need therapy for very long, perhaps only a few sessions. You may also want to read self-help books about healthy relationships and how to build self-esteem. If you’d like to find a therapist please click on this link that will take you to a directory of local mental health professionals. Thank you for your question and I wish you the best of luck.