If your dietary change contains some food material that you are allergic to, then it is probable that it could trigger some skin rashes. However, all your 3 infections seem like a primary bacterial infection and not an allergic response
. So, it is probably a coincidence is what I feel.
I hope you have taken the right antibiotics and also have completed the treatment. It is important to prevent the recurrence of infections.
Go for regular follow up to your treating doctor and make sure you are doing well.
I wish you good health.