There are a few different reasons why you might be experiencing a rash from weight lifting, and I'll outline them individually below.
Contact dermatitis occurs when your skin doesn't react well with another substance. This can include metals within free weights and weight benches.
Rashes from contact dermatitis are likely to be red and itchy, and may clear up on their own if you don't come into contact with the irritant again. You should seek medical advice if you think you have contact dermatitis as it can lead to other complications.
Humidity rashes
Poor ventilation in gyms is a common cause of rashes when lifting weights. With a lack of proper air flow, the body finds it difficult to cool itself down through perspiration, and this can lead to rashes and other skin conditions. Try to make sure you'll cool enough when lifting free weights, and performing other exercises.
Cellulitis
Another more serious skin condition that can occur after lifting weights is cullulitis. You're at risk of this if you've got a cut or wound that becomes infected with bacteria when you're exercising. Cellulitis leads to a rash, pain and can often produce swelling. Again, you should seek medical advice if you believe you've got cellulitis.
Here's a pretty interesting video documenting this young lady's experience with contact dermatitis. Maybe you'll share some of the symptoms?
