What you describe on your legs might be a rash, if so, this is a serious side effect of MTX and you should make your doctor aware of this as soon as possible.
Here is some information I got from WebMD about the side effects of Methotrexate:
All medicines may cause side effects, but many people have no, or minor, side effects. Check with your doctor if any of these most COMMON side effects persist or become bothersome when using Methotrexate:
Acne; chills and fever; dizziness; flushing; general body discomfort; hair loss; headache; infertility; irregular periods; itching; loss of appetite; lowered resistance to infection; miscarriage; nausea; sensitivity to sunlight; sore throat; speech impairment; stomach pain; swelling of the breast; unusual tiredness; vaginal discharge; vomiting.Seek medical attention right away if any of these SEVERE side effects occur when using Methotrexate:
Severe allergic reactions (rash; hives; itching; difficulty breathing; tightness in the chest; swelling of the mouth, face, lips, or tongue); black or bloody stools; blood in the urine; bone pain; calf pain/swelling; change in amount of urine; chest pain; confusion; dark urine; diarrhea; dry cough; enlarged glands; fatigue; fever or chills; inflammation of the pancreas (stomach tenderness, nausea, vomiting, fever, increased pulse rate); irregular heartbeat; mental changes; mouth sores; muscle weakness; persistent sore throat; red, swollen, or blistered skin; seizures; serious infection (herpes, hepatitis, blood infection); trouble breathing; unusual bleeding or bruising; unusual pain and discoloration of the skin; vision changes; vomit that looks like coffee grounds; yellowing of skin or eyes.
I hope that this answers some of your questions. Please let us know if you need more information.
Peace and Blessings